Question

List these solids in order from the one with least volume to the one with the greatest volume. A. A cube with edge 5 cm B. A cylinder with radius 4 cm and height 4 cm C. A square pyramid with base edges 6 cm and height 6 cm D. A cone with radius 4 cm and height 9 cm E. A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

Answer 1

The list in order from the one with least volume to the one with the greatest volume is

case C) A square pyramid with base edges 6 cm and height 6 cm

case A) A cube with edge 5 cm

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

case D) A cone with radius 4 cm and height 9 cm

case B) A cylinder with radius 4 cm and height 4 cm

Explanation:

To solve this problem calculate the volume of each solid

case A) A cube with edge 5 cm

The volume of a cube is equal to

`V=b^(3)`

where

b is the length side of the cube

substitute the value

`V=5^(3)=125\ cm^(3)`

case B) A cylinder with radius 4 cm and height 4 cm

The volume of a cylinder is equal to

`V=\pi r^(2) h`

substitute the value

`V=(3.14)(4)^(2) (4)=200.96\ cm^(3)`

case C) A square pyramid with base edges 6 cm and height 6 cm

The volume of a pyramid is equal to

`V=(1)/(3)Bh`

where

B is the area of the base

h is the height of the pyramid

Find the area of the base B

`B=6^(2)=36\ cm^(2)` ----> is a square

substitute the values

`V=(1)/(3)(36)(6)=72\ cm^(3)`

case D) A cone with radius 4 cm and height 9 cm

The volume of a cone is equal to

`V=(1)/(3)Bh`

where

B is the area of the base

h is the height of the cone

Find the area of the base B

`B=\pi r^(2)=(3.14)(4^(2))=50.24\ cm^(2)` ----> is a circle

substitute the values

`V=(1)/(3)(50.24)(9)=150.72\ cm^(3)`

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

The volume of a rectangular prism is equal to

`V=LWH`

substitute the values

`V=(5)(5)(6)=150\ cm^(3)`

therefore

The list in order from the one with least volume to the one with the greatest volume is

case C) A square pyramid with base edges 6 cm and height 6 cm

case A) A cube with edge 5 cm

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

case D) A cone with radius 4 cm and height 9 cm

case B) A cylinder with radius 4 cm and height 4 cm