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Geometric Modeling in Three Dimensions — Test Answers

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What is the volume of the shaded figure? Express the answer in terms of pi

A
324 pi ft cubed
B
261 pi ft cubed
C
288 pi ft cubed
D
252 pi ft cubed
7

A cylinder has a radius of 2 point 8 inches and a height of 2 point 4 inches. Which cylinder is similar?

A
Image with description A cylinder was radius 1.4 inches and height 1.2 inches.
B
Image with description A cylinder was radius 2.4 inches and height 2.8 inches.
C
Image with description A cylinder was radius 5.6 inches and height 4.2 inches.
D
Image with description A cylinder was radius 1.8 inches and height 1.4 inches.
8

Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism. How are the surface areas of the figures related?

A
The surface area of the larger prism is 4 times the surface area of the smaller prism.
B
The surface areas are the same.
C
The surface area of the larger prism is 2 times the surface area of the smaller prism.
D
The surface area of the larger prism is 8 times the surface area of the smaller prism.
11

Which expression represents the volume of the pyramid?

A
1 over 3 h 5 point 2 h cm cubed
B
1 fifth 5 point 2 h cm cubed
C
1 third 5 point 2 h cm cubed
D
1 over 5 h 5 point 2 h cm cubed
12

What is the volume of the composite figure? Express the answer in terms of pi

A
144 pi mm cubed
B
312 pi mm cubed
C
168 pi mm cubed
D
456 pi mm cubed
13

What is the volume of the cone?

A
24 pi cubic units
B
48 pi cubic units
C
32 pi cubic units
D
64 pi cubic units
14

The company wants to use the package that has the least amount of wasted space. The company should choose

A
the prism because it has approximately 11 point 6 in. cubed less wasted space than the cylinder.
B
the cylinder because it has approximately 14 point 1 in. cubed less wasted space than the prism.
C
the prism because it has approximately 14 point 1 in. cubed less wasted space than the cylinder.
D
the cylinder because it has approximately 11 point 6 in. cubed less wasted space than the prism.
15

Which expression represents the area of the base of the pyramid?

A
x squared square root of 3 units squared
B
6 x squared square root of 3 units squared
C
3 x squared square root of 3 units squared
D
4 x squared square root of 3 units squared
16

Which expression represents the volume, in cubic units, of the composite figure?

A
pi open paren 5 squared close paren 13 minus 1 third pi open paren 5 squared close paren 25
B
pi open paren 5 squared close paren 13 plus 1 third pi open paren 5 squared close paren 12
C
pi open paren 5 squared close paren 13 plus 1 third pi open paren 5 squared close paren 25
D
pi open paren 5 squared close paren 13 minus 1 third pi open paren 5 squared close paren 12

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