# Volume

• Oct 9th 2012, 08:20 AM
Farisco
Volume
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 AM
OriaG
Re: 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 AM
Soroban
Re: 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.

Code:

    -        * * *     :    *    :    *     :  *      :      *     :  *        :4      *     :          :     : * - - - - * - - - - *     :  \  4    :    4  /   10  \      :      /     :    \      :      /     :    \    :6    /     :      \    :    /     :      \  :  /     :        \  :  /     :        \ : /     :          \:/     -          *
We have a hemisphere with radius 4.
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: . $V \:=\:\tfrac{4}{3}\pi r^3$, where $r$ is the radius.

A half-sphere with radius 4 has volume: . $V \:=\:\tfrac{1}{2} \times \tfrac{4}{3}\pi(4^3) \:=\:\frac{128\pi}{3}$

A circular cone has volume: . $V \:=\:\tfrac{\pi}{3}r^2h\;\;(r = \text{radius, }\:h = \text{height})$

A cone with $r = 4,\,h=6$ has volume: . $V \;=\;\tfrac{\pi}{3}(4^2)(6) \:=\:32\pi$

The total volume is: . $\frac{128\pi}{3} + 32\pi \;=\;\boxed{\frac{224\pi}{3}\text{ cm}^3}$

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

. . . . $\boxed{2}\,\boxed{2}\,\boxed{4}\;\;\boxed{\times} \;\; \boxed{\pi}\;\;\boxed{\div}\;\;\boxed{3}\;\;\boxed {=}$

and we get: . $\boxed{234.5722515}$