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WorksheetsMath Major 124 (Plane and Solid Geometry)
Total questions: 50
Worksheet time: 44mins
Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.
441.66 cm2
467.64 cm2
519.60 cm2
493.62 cm2
A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the large pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.
430.70 cm3
573.26 cm3
473.77 cm3
516.14 cm3
The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle?
5.533 in.
5.335 in.
6.335 in.
7.335 in.
A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle formed by the sides of the hexagon.
36. 45 sq. m
63. 54 sq. m
45. 63 sq. m
54. 36 sq. m
In triangle ABC, angle C = 70o, A= 45o, AB = 40 m. What is the length of the median drawn from vertex A to side BC?
36.3 m
36.6 m
36.9 m
37.2 m
The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector?
89.5 cm2
58.9 cm2
59.8 cm2
85.9 cm2
What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm?
13.52
14.18
12.73
1564
Two complementary angles are in the ratio 2:1. Find the larger angle.
30°
60°
75°
15°
One side of a parallelogram is 10 m and its diagonals are 16 m and 24 m, respectively. Its area is:
156.8 sq. m.
185.6 sq. m.
158.7 sq. m.
142.3 sq. m.
The area of a rhombus is 132 square cm. if its shorter diagonal is 12 cm, the length of the longer diagonal is:
20 centimeter
21 centimeter
22 centimeter
23 centimeter
A regular octahedron has an edge 2m. Find its volume (in m3).
3.77
1.88
3.22
2.44
The central angle of a spherical wedge is 1 radian. Find its volume if its radius is 1 unit.
2/3
1/2
3/4
2/5
The bases of a right prism is a hexagon with one of each side equal to 6 cm. The bases are 12 cm apart. What is the volume of the right prism?
1211.6 cm3
2211.7 cm3
1212.5 cm3
1122.4 cm3
A circular cylinder with a volume of 6.54 cu. m is circumscribed about a right prism whose base is an equilateral triangle of side 1.25 m. What is the altitude of the cylinder in meters?
3.50
3.75
4.00
4.25
The height of a right circular base down is h. If it contains water to depth of 2h/3 the ratio of the volume of water to that of the cone is:
1:27
2:3
8:27
26:27
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
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
44
40.8
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
The surface area of the sphere is 4πr2. Find the percentage increase in its diameter when the surface area increases by 21%.
5%
10%
15%
20%
If a solid steel ball is immersed in an eight cm. diameter cylinder, it displaces water to a depth of 2.25 cm. the radius of the ball is:
3 cm
6 cm
9 cm
12 cm
A ___________is any closed, two-dimensional shape.
quadrilateral
figure
plane figure
solid figure
A ______________ is three-dimensional, having length, width and height.
plane figure
solid figure
triangle
quadrilateral
Any flat surface of a solid figure is called a ____.
edge
face
vertice
shape
The line segment where two faces of a solid figure intersect is called ______.
face
vertex
edge
The point at which two or more lines, line segments, or rays meet to form an angle. In solid figures, a _______ is the point at which three or more faces meet.
face
edge
vertex
What shape am I?
I have one circle and one curved side. My curved side surface meets at a sharp point. I have no edges.
cube
sphere
cone
triangular prism
What shape am I?
I have two congruent circles that are joined by a curved surface. I have no edges or vertices, but I can roll.
Cylinder
Sphere
Cone
Cube
What shape am I?
I am round with no edges, vertices, or edges.
Cyclinder
Sphere
Cone
Circle
What shape am I?
I have 6 faces , 12 edges, and 8 vertices. I have all the same shaped faces. All my edges are the same length.
Square Pyramid
Rectangular Prism
Cube
Cone
What shape am I?
I have 12 edges, 8 vertices, and 6 faces. I have both square and rectangular faces.
Rectangle
Cube
Square Pyramid
Rectangular Prism
What shape am I?
I have 5 faces, 8 edges, and 5 vertices. I have two different shaped faces.
Square Pyramid
Rectangular Prism
Cube
Cyclinder
What geometric figure will be created?
Cube
Rectangular Prism
Square Pyramid
Cone
What geometric shape will be created?
Cube
Rectangular Prism
Squares
Cyclinder
What combinations of shapes would you need to create a cube?
6 square faces
6 rectangle faces
4 squares and 2 rectangles faces
4 rectangles and 2 square faces
What combinations of shapes would you need to create a rectangular prism?
6 square faces
6 rectangle faces
4 squares and 2 rectangles faces
4 rectangles and 2 square faces
(a) is the sum of all the areas of the lateral faces and the base of the solid.
The solid that has at least three faces that are rectangles is called (a) .
A prism has two bases while the pyramid has only (a) base.
(a) refers to the 3-dimensional space enclosed by a surface.
They have the same volume.
Cylinder A
Cylinder B
There is not enough information to determine.
V=Bh
S=Ph+2B
The big B in the equations for volume and surface area means...
The AREA of the BASE.
The Circumference of the BASE.
The PERIMETER of the BASE.
the distance between the two bases.
Is this problem asking about Lateral or Total surface area?
If all of the dimensions of a triangular prism decreased by 1/3, how much would the volume decrease by?
1/27
1/9
1/3
1/6
Describe the position of the plane.
Vertical
Horizontal
Diagonal
A right cylinder is cut perpendicular to its base. The shape of the cross section is a
circle
cylinder
rectangle
triangular prism
A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what can not be the three-dimensional object?
