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Geometry Review #6 3-D Figures

Total questions: 50

Worksheet time: 1hrs 21mins

Name
Class
Date
1.

The arrow shown is on a sign. If it cost $2 per square inch to paint the sigh what is the smallest total cost of 5 signs?

a)

$170

b)

$230

c)

$400

d)

$520

e)

$610

2.

Find the area of the shaded region:

a)

350 cm2

b)

137.5 cm2

c)

212.5 cm2

d)

484.2 cm2

e)

75 cm2

3.

Find the area of the figure:

a)

276 cm2

b)

114 cm2

c)

247 cm2

d)

390 cm2

e)

68 cm2

4.

Find the area of the figure

a)

43 in2

b)

102 in2

c)

37 in2

d)

90 in2

e)

31 in2

5.

The diagram shows the spot on a basketball court called the “key”. What is the area of the key? Use 3.14 for π.

a)

284.52 ft2

b)

228 ft2

c)

317 ft2

d)

116.71 ft2

e)

456 ft2

6.

Lucia has a triangular prism that has a length of 6cm and the width of 4cm and the height is 8cm. What is the volume

a)

96cm³

b)

54cm³

c)

80cm³

d)

24cm³

e)

192cm³

7.

What is the area of the base of the pyramid?

a)

B= 1800 mm3

b)

B= 150 mm2

c)

B=900 mm2

d)

B=1200 mm3

e)

B=600 mm3

8.

Find the volume to the nearest hundredth using 3.14 instead of Pi.

a)

418.00 cm3

b)

139.33 cm3

c)

130.62 cm3

d)

1671.98 cm3

e)

532.48 cm3

9.

Find the volume to the nearest hundredth using 3.14 instead of Pi.

a)

12.56 ft3

b)

37.68 ft3

c)

18.84 ft3

d)

6.28 ft3

e)

12.00 ft3

10.

Find the volume.

a)

151.2 yd3

b)

163.7 yd3

c)

179.1 yd3

d)

186.3 yd3

e)

80.0 yd3

11.

Find the volume.

a)

147

b)

588

c)

84

d)

294

e)

882

12.

Which equation would you use to find the volume of this composite figure?

a)

83 + 4/3π(8)³

b)

83 + 4/3π(4)³

c)

83 + (1/2)(4/3)π(4)³

d)

82 + 4/3π(8)³

e)

82+(1/2)82π

13.

Find the volume of the roll of duct tape.

a)

7.2

b)

8.0

c)

9.4

d)

15.7

e)

21.3

14.

Find the approximate Volume.

a)

1412.4

b)

965.2

c)

1123.6

d)

1348.6

e)

611.5

15.

Landon used a semicircle, rectangle, and a right triangle to form the figure shown. Which is the best estimate of the area of the figure?

a)

52 cm2

b)

44 cm2

c)

26 cm2

d)

38 cm2

e)

There is not enough information, the hypotenuse of the right triangle is needed to solve.

16.

Find the volume of the Sphere. Use 3.14 for pi.

a)

337.3 ft3

b)

137.2 ft3

c)

274.4 ft³

d)

205.8 ft³

e)

102.89 ft³

17.

Soda is sold in aluminum cans that measure

4.83 inches in height and 2.6 inches in diameter. What is the volume? Round to the nearest hundredth.

a)

25.64 in3

b)

26.00 in3

c)

19.73 in3

d)

95.28 in3

e)

32.65 in3

18.

What is the name of this 3D solid?

a)

Hexagonal Prism

b)

Hexagonal Pyramid

c)

Pentagonal Pyramid

d)

Pentagonal Prism

e)

Not enough information

19.

What is the volume of the shape?

a)

540 cm3

b)

810 cm3

c)

1080 cm3

d)

4320 cm3

e)

Not enough information to solve the volume

20.

Jerry has a new slanted coke can design for his marketing campaign. He knows the volume and height he wants for his display but he wants to figure out the diameter of the display. What is the diameter of his can display in the picture?

a)

4cm

b)

6cm

c)

8cm

d)

12cm

e)

16 cm

21.

Given the two prisms in the picture in the picture which of the statements is true according to Cavalier's principal.

a)

The Oblique Prism has a longer slant height so the volume is greater than the Right Prism

b)

The Right Prism has a longer slant height so the volume is greater than the Oblique Prism

c)

The Oblique Prism has 2 different bases and when taking the average of these bases and multiplying them by the height the volume is greater than the Right Prism

d)

The Oblique Prism has 2 different bases and when taking the average of these bases and multiplying them by the height the volume is less than the Right Prism

e)

Both types of Prisms have the same base and height so there volume is the same

22.

What is the volume of the shape?

a)

V= 28,938.24 cm3

b)

V= 2,712.96 cm3

c)

V= 7,234.56 cm3

d)

V= 3,617.28 cm3

e)

V= 603.19 cm3

23.

A table tennis ball has a diameter of 40 mm. What is the approximate volume of the table tennis ball in cubic millimeters?

a)

1,676 mm3

b)

18,850 mm3

c)

33,510.3 mm3

d)

268,083 mm3

e)

Not enough information to solve the volume

24.

Veal finds a gold colored rock in a river. It has a mass of 9.65 grams and a volume of 0.5 cm3. What is the density of the rock?

a)

10.15 g/cm3

b)

19.3 g/cm3

c)

9.15 g/cm3

d)

4.825 g/cm3

e)

9.65 g/cm3

25.

Describe the cross section.

a)

trapezoid

b)

triangle

c)

rectangle

d)

square

e)

Trapezoid

26.

What shape will the horizontal cross-section of a sphere be?

a)

Dome

b)

Circle

c)

Ellipse

d)

Rectangle

e)

Prism

27.

What shape will the horizontal cross-section of a cone be?

a)

Semi Circle

b)

Circle

c)

Parabola

d)

Triangle

e)

Oval (Ellipse)

28.

Describe the cross section.

a)

rectangle

b)

trapezoid

c)

oval (ellipse)

d)

parallelogram

e)

circle

29.

What shape will the angled cross-section of a rectangular pyramid be?

a)

Triangle

b)

Rectangle

c)

Trapezoid

d)

Square

e)

rhombus

30.

Jack has a rock. The rock has a mass of 14g and a volume of 2cm3. What is the density of the rock?

a)

7 mL

b)

7 g/cm3

c)

28 g/cm3

d)

1/7 g/cm3

e)

16g+cm3

31.

If the mass of an unknown substance is 105 grams and the volume is 35 cm.3 What would be its density? (round)

a)

2.7

b)

3.5

c)

4.0

d)

3.0

e)

.3

32.

If the density of a bar of gold is 19.3 g/cm3and you cut it into 4 pieces, what is the density of each piece of gold?

a)

4.825 g/cm3

b)

9.65 g/cm3

c)

19.3 g/cm3

d)

38.6 g/cm3

e)

.21 g/cm3

33.

A right hexagonal prism is shown. A two dimensional cross section that is perpendicular to the base is taken from the prism. Which figure describes the two-dimensional cross section?

a)

Triangle

b)

Rectangle

c)

Pentagon

d)

Hexagon

e)

Trapezoid

34.

The cross section of a regular pyramid contains the altitude of the pyramid. The shape of this cross section is a

a)

circle

b)

square

c)

triangle

d)

rectangle

e)

trapezoid

35.

A plane intersects a hexagonal prism. The plane is perpendicular to the base of the prism. Which two dimensional figure is the cross section to the plane intersecting the prism?

a)

triangle

b)

trapezoid

c)

hexagon

d)

rectangle

e)

trapezoid

36.

A two-dimensional cross section is taken of a three-dimensional object. If the cross section is a triangle, what cannot be the three-dimensional object?

a)

cone

b)

cylinder

c)

pyramid

d)

rectangular prism

e)

triangular prism

37.

Which figure can have the same cross section as a sphere?

a)
b)
c)
d)
e)

Not enough information

38.

Which drawing can not be a cross section of a cone?

a)
b)
c)
d)
e)

All of these are cross sections of a cone

39.

A student has a rectangular postcard that he folds in half lengthwise. Next he rotates it continuously about the folded edge. Which three dimensional object below is generated by the rotation?

a)
b)
c)
d)
40.

Which object is formed when right triangle RST shown is rotated around leg RS

a)

a cylindar

b)

a pyramid with a square base

c)

an isosceles triangle

d)

a right triangle

e)

a cone

41.

If the rectangle is continuously rotated about side w, which solid figure is formed?

a)

sphere

b)

pyramid

c)

rectangular prism

d)

cone

e)

cylinder

42.

Triangle ABC represents a metal flag on pole AD, as shown in the accompanying diagram. On a windy day the triangle spins around the pole so fast that it looks like a three-dimensional shape. Which shape would the spinning flag create?

a)

Oblique Circular Cylinder

b)

Sphere

c)

Pyramid

d)

Right Circular Cylindar

e)

Cone

43.

If an equilateral triangle is continuously rotated around one of its medians, which 3-dimensional object is generated?

a)

cone

b)

pyramid

c)

prism

d)

sphere

e)

triangular pyramid

44.

Circle O is centered at the origin. In the diagram below, a quarter of circle O is graphed. Which three-dimensional figure is generated when the quarter circle is continuously rotated about the y-axis?

a)

cone

b)

sphere

c)

cylinder

d)

hemisphere

e)

crescent

45.

In the diagram below, right triangle ABC has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around side AB?

a)

24π

b)

32π

c)

48π

d)

96π

e)

144π

46.

As of 2015, the most densely populated state in the US was New Jersey. The 2015 population of New Jersey was 8,957,907 people with 1218.1 people per square mile. Which choice is the approximate land area of the state of New Jersey to the nearest square mile?

a)

7135 sq. mi.

b)

7354 sq. mi

c)

10912 sq. mi.

d)

12354 sq. mi.

e)

not enough information

47.

Ninety-eight cut boulders are being brought in to help prevent further erosion on a portion of this coastline. Each boulder has been roughly cut into a cube with sides of length 0.8 meters. The stone in the boulders has an average density of 3000 Kg/m3. A dump truck with a carrying capacity of 28,000 pounds is used to transport the boulders to the coastline. How many trips will the truck need to make to transport all of the boulders? Assume the truck does not exceed its carrying capacity.

a)

10

b)

11

c)

12

d)

13

e)

14

48.

Jason is drinking a soda from a can ridiculously large can that has a radius of 5 in and a height of 43 in. He has already drank 1/4 of the soda, how much soda is still remaining in the can? Leave the answer in terms of π.

a)

1075π

b)

268.75π

c)

430π

d)

806.25π

e)

1075π

49.

A dense patch of dandelions can contain 250 dandelions per square foot. Approximately how many dandelions could be in a circular area with a 6 foot diameter?

a)

1500 dandelions

b)

3750 dandelions

c)

28260 dandelions

d)

7065 dandelions

e)

14130 dandelions

50.

The dimensions of grain storage bins in the shape of a cylinder and a rectangular prism are shown. Which measurement is closest to the difference between the volumes of the 2 bins?

a)

24,280 cubic feet

b)

16,430 cubic feet

c)

11,720 cubic feet

d)

4,480 cubic feet

e)

16,000 cubic feet