# Find the volume of the solid Question

• Dec 7th 2006, 05:33 PM
killasnake
Find the volume of the solid Question
I do not know how to do these problem should some one help

Quote:

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

________
and

Quote:

You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h=3900 and a square base with side s=1470. To impress your Egyptian subjects, find the volume of the pyramid.

___________
• Dec 7th 2006, 05:39 PM
Quick
Quote:

Originally Posted by killasnake
I do not know how to do these problem should some one help
Quote:

You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h=3900 and a square base with side s=1470. To impress your Egyptian subjects, find the volume of the pyramid.

___________

A pyramid's volume is: $V=\frac{1}{3}Ah$

where: $A=\text{Area of the Base}$

And: $h=\text{The Height of the Pyramid}$

So the area of the base is obviously $A=s^2=1470^2=2160900$

So then find the volume :)
• Dec 7th 2006, 07:33 PM
killasnake
Thank you for the help Quick, Any ideas how to do the first one?
• Dec 8th 2006, 03:30 AM
Soroban
Hello, killasnake!

I must assume that you know about Volumes of Revolution . . .

Quote:

Find the volume of the solid obtained by rotating the region bounded by:
. . $y = x^6,\;y=1$, about $y=2$

Code:

                  |                 2|       - - - - - - + - - - - - -                   |                   |       *- - - - - + - - - - -*(1,1)         *::::::::|::::::::*             *:::::|:::::*       - - - - - - * - - - - - - -                   |

$V \;=\;2 \times \int^1_0\left[(2-x^6)^2 - (2 - 1)^2\right]\,dx$