WorksheetsBSME SET #7
Total questions: 95
Worksheet time: 32mins
If the edge of a cube is doubled, which of the following is incorrect?
The lateral area will be quadrupled
The volume is increased 8 times
The diagonal is doubled
The weight is doubled
The volume of a cube is reduced by how much if all sides are halves?
1 / 8
5 / 8
6 / 8
7 / 8
Each side of a cube is increased by 1%. By what percent is the volume of the cube increased?
23.4%
33.1%
3%
34.56%
If the edge of a cube is increased by 30%, by how much is the surface area increased?
67
69
63
65
Find the approximate change in the volume of a cube of side x inches caused by increasing its side by 1%
0.3x³ cu. in.
0.1x³ cu. in.
0.02 cu. in.
0.03x³ cu. in.
A rectangular bin 4 feet long, 3 feet wide, and 2 feet high is solidly packed with bricks whose dimensions are 8 in. by 4 in. by 2 in. The number of bricks in the bin is:
68
386
648
956
Find the total surface area of a cube of side 6 cm.
214 sq. cm.
216 sq. cm.
226 sq. cm.
236 sq. cm.
The space diagonal of a cube is 4√3 m. Find its volume.
16 cubic meters
48 cubic meters
64 cubic meters
86 cubic meters
A reservoir is shaped like a square prism. If the area of its base is 225 sq. cm., how many liters of water will it hold?
3.375
3375
33.75
337.5
Find the angle formed by the intersection of a face diagonal to the diagonal of a cube drawn from the same vertex.
A. 35.26º
B. 32.56º
C. 33.69º
D. 42.23º
The space diagonal of a cube is 6 m. The total surface area of the cube is:
60
66
72
78
The base edge of a regular hexagonal prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm.
1563.22 cm³
1058.89 cm³
1896.37 cm³
1122.12 cm³
The base edge of a regular pentagonal prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm.
743.22 cm³
786.89 cm³
587.45 cm³
842.12 cm³
The bases of a right prism is a hexagon with one side 6 cm long. If the volume of the prism is 450 cc, how far apart are the bases?
5.74 cm
3.56 cm
4.11 cm
4.81 cm
A trough has an open top 0.30 m by 6 m and closed vertical ends which are equilateral triangles 30 cm on each side. It is filled with water to half its depth. Find the volume of the water in cubic meters.
0.058 cm³
0.046 cm³
0.037 cm³
0.065 cm³
Determine the volume of a right truncated prism with the following dimensions: Let the corner of the triangular base be defined by A, B, and C. The length AB = 10 feet, BC = 9 feet, and CA = 12 feet. The sides at A, B and C are perpendicular to the triangular base and have the height of 8.6 feet, 7.1 feet, and 5.5 feet, respectively.
413 ft³
311 ft³
313 ft³
391 ft³
The volume of a regular tetrahedron of side 5 cm is:
A. 13.72 cu. cm
C. 15.63 cu. cm
B. 14.73 cu. cm
D. 17.82 cu. cm
A regular hexagonal pyramid whose base perimeter is 60 cm has an altitude of 30 cm. The volume of the pyramid is:
A. 2958 cu. cm.
C. 2859 cu. cm.
B. 2598 cu. cm.
D. 2589 cu. cm.
A frustum of a pyramid has an upper base 100 m by 10 m and a lower base of 80 m by 8 m. If the altitude of the frustum is 5 m, find its volume.
4567.67 cu. m.
3873.33 cu. m.
4066.67 cu. m.
2345.98 cu. m.
The altitude of the frustum of a regular rectangular pyramid is 5m the volume is 140 cu. m. and the upper base is 3m by 4m. What are the dimensions of the lower base in m?
9 x 10
6 x 8
4.5 x 6
7.50 x 10
The frustum of a regular triangular pyramid has equilateral triangles for its bases. The lower and upper base edges are 9m and 3m, respectively. If the volume is 118.2 cu.m., how far apart are the base?
9 m
8 m
7 m
10 m
A cylindrical gasoline tank, lying horizontally, 0.90 m. in diameter and 3 m long is filled to a depth of 0.60 m. How many gallons of gasoline does it contain?
250
360
358
270
A closed cylindrical tank is 8 feet long and 3 feet in diameter. When lying in a horizontal position, the water is 2 feet deep. If the tank is in the vertical position, the depth of water in the tank is:
5.67 m
5.82 ft
5.82 m
5.67 ft
A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the cylinder is 6.283 cu. m. Find its altitude in m.
5 m
4.5 m
69.08 m
4 m
If 23 cubic meters of water are poured into a conical vessel, it reaches a depth of 12 cm. How much water must be added so that the depth reaches 18 cm.?
95 cubic meters
100 cubic meters
54.6 cubic meters
76.4 cubic meter
The height of a right circular cone with circular base down is h. If it contains water to a depth of 2h/3 the ratio of the volume of water to that of the cone is
1:27
23
8:27
26:27
A right circular cone with an altitude of 9m is divided into two segments, one is a smaller circular cone having the same vertex with an altitude of 6m. Find the ratio of the volume of the two cones.
A. 19:27
B. 23
C. 13
D. 8:27
A conical vessel has a height of 24 cm. and a base diameter of 12 cm. It holds water to a depth of 18 cm. above its vertex. Find the volume of its content in cc.
387.4
381.7
383.5
385.2
A right circular cone with an altitude of 8 cm is divided into two segments. One is a smaller circular cone having the same vertex with volume equal to 1/4 of the original cone. Find the altitude of the smaller cone.
4.52 cm
6.74 cm
5.04 cm
6.12 cm
The slant height of a right circular cone is 5m long. The base diameter is 6m. What is the lateral area in sq. m?
37.7
47.12
44
40.8
A right circular cone has a volume of 128/3 cm³ and an altitude of 8 cm. The lateral area is:
165 cm²
12√5 cm²
16 cm²
15 cm²
The volume of a right circular cone is 36. If its altitude is 3, find its radius.
3
4
5
6
A cone and hemisphere share base that is a semicircle with radius 3 and the cone is inscribed inside the hemisphere. Find the volume of the region outside the cone and inside the hemisphere.
24.874
27.284
28.274
28.724
A cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in diameter with a central angle of 210. What is the volume of the cone?
13,602 cc
13,504 cc
13,716 cc
13,318 cc
A cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in diameter with central angle of 150°. Find the volume of the cone in cc.
7733
7722
7744
7711
A chemist's measuring glass is conical in shape. If it is 8 cm deep and 3 cm across the mouth, find the distance on the slant edge between the markings for 1 cc and 2 cc.
0.82 cm
0.79 cm
0.74 cm
0.92 cm
The base areas of a frustum of a cone are 25 sq. cm. and 16 sq. cm., respectively. If its altitude is 6 cm., find its volume.
120 cm³
122 cm³
129 cm³
133 cm³
How far from a vertex is the opposite face of a tetrahedron if an edge is 50 cm long?
38.618 cm
40.825 cm
39.421 cm
41.214 cm
A truncated prism has a horizontal triangular base ABC, AB = 10 cm, BC = 12 cm, CA = 8 cm. The vertical edges through A, B, and C are 20 cm, 12 cm, and 18 cm long respectively. Determine the volume of the prism in cc.
661
559
685
574
A lateral edge of the frustum of a regular pyramid is 1.8 m long. The upper base is a square 1 m × 1 m and the lower base 2.4 m × 2.4 m. Determine the volume of the frustum in m³.
4.6
3.3
5.7
6.5
A solid cylinder 30 cm in diameter and 50 cm high is floating in water with its axis vertical. A solid sphere is dropped into the cylinder, causing the water level to rise by 10 cm. What is the radius of the cylinder?
A. 12.14
B. 9.08
C. 10.28
D. 11.55
A conical vessel one meter in diameter at the top and 60 cm high holds salt at a depth of 36 cm from the bottom. How many cc of salt does it hold?
37,214
33,929
35,896
31,574
An open-top cylindrical tank is made of a metal sheet having an area of 43.82 m². If the diameter is 2/3 the height, what is the height of the tank?
3.24 m
2.43 m
4.23 m
5.23 m
The lateral area of a right circular cone is 386 cm². If its diameter is one-half its altitude, determine its altitude in centimeters.
24.7
17.4
18.9
22.5
The surface area of a regular tetrahedron is 173.2 cm². What is its altitude?
A. 8.2 cm
B. 9.6 cm
C. 7.2 cm
D. 6.5 cm
A cube of edge 25 cm is cut by a plane containing two diagonally opposite edges of the cube. Find the area of the section thus formed in cm².
812.3
912.7
841.2
883.9
A swimming pool is rectangular in shape, 12 m long and 5.5 m wide. It is 1 m deep at one end and 3.6 m deep at the other. Water from a full cylindrical reservoir 3.6 m in diameter and 10 m deep is emptied into the pool. Find the depth of water at the deep end.
2.912 m
2.695 m
2.842 m
2.754 m
Two vertical conical tanks (both inverted) are connected by a horizontal pipe. One tank, initially full of water, has an altitude of 6 m and a diameter of 7 m. The other, initially empty, has an altitude of 9 m and a diameter of 8 m. Find the level to which the water will ultimately rise in the empty tank (neglect water in the pipe).
4.254 m
3.257 m
4.687 m
5.151 m
A sphere of radius 5 cm and a right circular cone of radius 5 cm and height 10 cm stand on a plane. How far from the base of the cone must a cutting plane (pass parallel to the base of the cone) pass in order to cut the solids in equal circular sections?
1 cm
3 cm
5 cm
2 cm
A pyramid whose altitude is 7 ft weighs 800 pounds. At what distance from its base must it be cut by a plane parallel to its base so that two solids of equal weight will be formed?
3.500 ft
5.556 ft
1.444 ft
2.856 ft
What is the surface area of a sphere whose volume is 36 cu. m?
52.7m²
48.7m²
46.6m²
54.6m²
If the surface area of the sphere is increased by 21%, its volume is increased by:
A. 13.31%
B. 33.1%
C. 21%
D. 30%
The surface area of a sphere is 4πr². Find the percentage increase in its diameter when the surface area increases by 21%.
5%
10%
15%
20%
Find the percentage increase in volume of a sphere if its surface is increased by 21%
30.2%
33.1%
34.5%
30.9%
The volume of a sphere is increased by how much if its radius is increased by 20%
32.6%
33%
44%
72.8%
Given two spheres whose combined volume is known to be 819 cu.m. their radii are in the ratio 3:4, what is the volume of the smaller sphere?
576 cu.m
243 cu.m
343 cu.m
476 cu.m
How much will the surface area of a sphere be increased if its radius increased by 5%?
15.5%
12.5%
10.25%
The volume of the sphere is 904.78 cu.m. Find the volume of the spherical segment of height 4m.
234.57 cu.m
256.58 cu.m
145.69 cu.m
124.58 cu.m
A sphere of a radius r just fits into a cylindrical container of radius r and altitude 2r. Find the empty space in the cylinder.
(8/9)πr³
(20/27)πr³
(4/5)πr³
(2/3)πr²
If a solid steel ball is immersed in an eight cm. diameter cylinder, displaces water to a depth of 2.25 cm. The radius of the ball is:
3cm
6cm
9cm
12cm
The diameter of two spheres are in the ratio 2:3. If the sum of their volume is 1,260 cu.m, the volume of the larger sphere is:
972 cu. m
927 cu. m
856 cu. m
865 cu. m
A hemispherical bowl of radius 10cm is filled with water to such as that the water surface area is equal to 75π sq. cm. The volume of water is:
625/3 cm³
625π/3cm³
625π/2cm³
625π cm³
A water tank is in the form of a spherical segment whose base radii are 4m and 3m and whose altitude is 6m. The capacity of the tank in gallons is:
91,011
92,011
95,011
34,872
Find the volume of a spherical sector of altitude 3 cm and radius 5 cm.
75π cu. Cm.
100π cu. Cm.
50π cu. Cm.
25π cu. Cm.
A water tank is in the form of a spherical segment whose base radii are 4m and 3m and whose altitude is 6m. The capacity of the tank in gallons is:
91,011
92,011
95,011
348.72
How far from the center of a sphere of a radius 10 cm should a plane be passed so that the ratio of the areas of two zones is 3:7.
3 cm
4 cm
5 cm
6 cm
A 2-m diameter spherical tank contains 1396 liters of water. How many liters of water must be added for the water to reach a depth of 1.75 m?
2613
2542
2723
2472
Find the volume of a spherical segment of radius 10 m and altitude 5 m.
654.5 cu. M.
659.8 cu. M
675.2 cu. M.
680.5 cu. M.
Find the volume of a spherical wedge of radius 10 cm and central angle 50°.
425.66 sq. M.
581.78 sq. M.
431.25 sq. M.
444.56 sq. M.
Determine the area of the zone of a sphere of radius 8 in. and altitude 12 in.
192π sq. In.
198π sq. In.
185π sq. In.
195π sq. In.
The corners of a cubical block touch the closed spherical shell that encloses it. The volume of the box is 2744 cc. What volume in cc, inside the shell is not occupied by the block?
1356 cm³
4721 cm³
3423 cm³
7623 cm³
A cubical container that measures 2 inches on each side is tightly packed with 8 marbles and is filled with water. All 8 marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are of the same size. What is the volume of water in the container?
0.38 cu. In.
2.5 cu. In.
3.8 cu. In.
4.2 cu. In.
The volume of the water is a spherical tank is 1470.265 cm³. Determine the depth of water if the tank has a diameter of 30 cm.
8
6
4
10
The volume of water in a spherical tank having a diameter of 4 m. Is 5.236 m³. Determine the depth of the water on the tank.
1.0
1.2
1.4
1.6
A mixture compound from equal parts of two liquids, one white and the other black, was placed in a hemispherical bowl. The total depth of the two liquids is 6”. After standing for a short time the mixture separated the white liquid settling below the black. If the thickness of the segment of the black liquid is 2”, Find the radius of the bowl in inches.
7.53
7.33
7.73
7.93
20.5 cubic meters of water is inside a spherical tank whose radius is 2m. Find the height of the water surface above the bottom of the tank, in m.
2.7
2.3
2.5
2.1
The volume of the sphere is 36π cu. m. The surface area of this sphere in sq. m. is:
36π
24π
18π
12π
Spherical balls 1.5 cm in diameter are packed in a box measuring 6 cm by 3 cm by 3 cm. If as many balls as possible are packed in the box, how much free space remains in the box?
28.41 cc
20.47 cc
29.87 cc
25.73 cc
A solid has a circular base of radius r. Find the volume of the solid if every plane perpendicular to a given diameter is a square.
16r³/3
6r³
5r³
19r³/3
A solid has circular base of diameter 20 cm. Find the volume of the solid if every cutting plane perpendicular to the base along a given diameter is an equilateral triangle.
2514 cc
2107 cc
2309 cc
2847 cc
The base of a certain solid is a triangle of base b and altitude h. If all sections perpendicular to the altitude of the triangle are regular hexagons, find the volume of the solid.
½ √(3) b²h
2√(3) b²h
√(3) b²h / 3
√(3) b²h
The volume generated by the circle x² + y² + 4x - 6y - 12 = 0 revolved about the line 2x - 3y - 12 = 0 is;
3242 cubic units
3342 cubic units
3452 cubic units
3422 cubic units
The volume generated by rotating the curve 9x2+4y2=36 about the line 4x+3y=20 :
48π
58π²
42π
48π²
Find the volume generated revolving the area bounded by the ellipse 9y2+4x2=1 about the line x = 3
347.23 cu. Units
378.43 cu. Units
355.31 cu. Units
389.51 cu. Units
The area in the second quadrant of the circle x² + y² = 36 is revolved about the line y + 10 = 0. What is generated?
2218.6
2228.8
2233.4
2208.5
A square area of edge “a” revolves about a line through one vertex, making an angle θ with an edge and not crossing the square. Find the volume generated.
3π a³ (sin θ + cos θ)
Π a³ (sin θ + cos θ) / 2
2π a³ (sin θ + cos θ)
π a³ (sin θ + cos θ)
Given an ellipse whose semi-major axis is 6 cm. And semi-minor axis is 3 cm. What is the volume generated if it is revolved about the minor axis?
36π cu. Cm.
72π cu. Cm.
96π cu. Cm.
144π cu. Cm.
A square hole 2” × 2” is cut through a 6-inch diameter log along its diameter and perpendicular to its axis. Find the volume of wood that was removed.
27.32 cu. In.
23.54 cu. In.
21.78 cu. In.
34.62 cu. In.
Find the radius of the spherical wedge whose volume is 12 cu. M. With a central angle of 1.8 radians.
2.36 m
2.73 m
2.52 m
2.15 m
By using Pappus Theorem, determine the volume generated by revolving the area in the first and second quadrants bounded by the ellipse 4x² + 25y² = 100 and the x-axis, about the x-axis.
85.63
93.41
95.35
83.78
Determine the volume of a spherical wedge of radius 2. M and a central angle of 1.25 radians.
6.67 m³
8.64 m³
9.85 m³
5.74 m³
Find the volume generated by revolving the triangle whose vertices are (2, 2), (4, 8), and (6, 2) about the line 3x – 4y – 240.
365.45
498.12
543.65
422.23
A light bulb is placed at a certain distance from the surface of a spherical globe of radius 20 cm. If it illuminates one-third of the total surface of the globe, how far is it from the surface?
30 cm
35 cm
60 cm
40 cm
A conoid has a circular base of radius 25 cm and an altitude of 30 cm. Find its volume in cc.
32,457
29,452
24,486
18,453
A sphere having a diameter of 30 cm. Is cut into 2 segments. The altitude of the first segment is 8 cm. What is the ratio of the volume of the second segment to that of the first?
3.2
4.7
5.8
2.5
