A cone is attached to a hemisphere of radius 4 cm. If the total height of the object is 10 cm, find its volume.

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- Oct 9th 2012, 08:20 AMFariscoVolume
**A cone is attached to a hemisphere of radius 4 cm. If the total height of the object is 10 cm, find its volume.**

- Oct 9th 2012, 08:29 AMOriaGRe: Volume
Let's calculate the volume of the cone and the volume of the hemisphere seperatly and then add them. I will be accurate to 2 points after the decimal point.

Hemisphere: V = (2/3)*pi*r^3 = 128*pi/3 = 134.04

If the height of the entire object is 10, and the radius of the hemisphere is 4, then the height of the cone is 10 - 4 = 6.

Cone: V = (1/3)*pi*r^2*h = 32*pi = 100.53

Vcone + Vhemisphere = 134.04 + 100.53 = 234.57 - Oct 9th 2012, 11:37 AMSorobanRe: Volume
Hello, Farisco!

Quote:

A cone is attached to a hemisphere of radius 4 cm.

If the total height of the object is 10 cm, find its volume.

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We have cone with radius 4 and height 6.

You should be able to find the total volume

. . without a calculator and without rounded-off decimals.

A sphere has volume: . , where is the radius.

A half-sphere with radius 4 has volume: .

A circular cone has volume: .

A cone with has volume: .

The total volume is: .

If you want a decimal,is the time to crank it out:*now*

. . . .

and we get: .