Question

What is the volume of the composite figure? (Round to the nearest hundredth. Use 3.14 for Pi.)

V cone = one-third pi r squared h. V sphere = four-thirds pi r cubed.

A half sphere and cone. Both have a radius of 4 centimeters. The cone has a height of 15 centimeters.

150.72 cubic centimeters
276.32 cubic centimeters
385.17 cubic centimeters
519.15 cubic centimeters

Answer 1

The volume of composite figure is 385.17 cubic centimeters

Explanation:

EDG 2020

Answer 2

The volume of composite figure is 385.17 cubic centimeters, if a half sphere and cone have a radius of 4 centimeters and height of 15 centimeters.

Explanation:

The given is,

Composite figure is combination of a half sphere and cone

Both have a radius of 4 centimeters

The cone has a height of 15 centimeters

Step:1

Volume of composite figure = Volume of half sphere + Volume of cone

Step:2

Formula for volume of semi sphere,

`Volume of half sphere, V_(Half sphere) = (2)/(3) \pi r^(3)`

Where, r - Radius of Half sphere,

From given, r = 4 centimeters

`V_(Half sphere) = (2)/(3) \pi 4^(3)`

`= (0.6667) (3.14) (64)` (∵
`\pi` = 3.14 )

`V_(Half sphere)` = 133.9733 cubic centimeters

Formula for volume of cone,

`Volume of cone, V_(cone) = (1)/(3) \pi r^(2) h`

where, r - Radius of cone

h - Height of cone

From given,

r = 4 centimeters

h = 15 centimeters

Volume of cone,

`V_(cone) = (1)/(3) \pi 4^(2)(15)`

`= (0.333333) (3.14)(16)(15)` (∵
`\pi` = 3.14 )

`V_(cone)`
`= 251.1997` cubic centimeters

Step:3

Volume of composite figure = 133.9733 + 251.1997

Volume of composite figure = 385.17 cubic centimeters

Result:

The volume of composite figure is 385.17 cubic centimeters, if a half sphere and cone have a radius of 4 centimeters and height of 15 centimeters.