# Height of Pyramid

• Nov 20th 2008, 06:30 PM
magentarita
Height of Pyramid
If the volume of the pyramid is 192 yd^3 and the area of the base is 64 yd^2, what is the height of the pyramid?
• Nov 21st 2008, 05:27 PM
Rapha
Hi mate

Quote:

Originally Posted by magentarita
If the volume of the pyramid is 192 yd^3 and the area of the base is 64 yd^2, what is the height of the pyramid?

I guess it is just

$\displaystyle V = \frac{1}{3} Bh$ , where B is the area

V = 192 yd^3 $\displaystyle ;V = \frac{1}{3} Bh$ where B is the area
B = 64 yd^2

=> $\displaystyle V = \frac{1}{3} Bh$

=> $\displaystyle 192 \ yd^3 = \frac{1}{3} 64 \ yd^2 *h$

=> $\displaystyle h = 3*192 \ yd^3 / (64 \ yd^2) = 9 \ yd$

Rapha
• Nov 21st 2008, 05:39 PM
David24
Quote:

Originally Posted by magentarita
If the volume of the pyramid is 192 yd^3 and the area of the base is 64 yd^2, what is the height of the pyramid?

By defintion, the volume of a square based pyramid is given by

Vol = (1/3) x Perpendicular Height x Area of Base

Subbing in the known parameters yields

192 = (1/3) x Perpendicular Height x 64

Thus,

the Perpendicular Height = (3 x 192) / 64

Hope this helps,

Regards,

David
• Nov 21st 2008, 06:40 PM
magentarita
ok............
Quote:

Originally Posted by Rapha
Hi mate

I guess it is just

$\displaystyle V = \frac{1}{3} Bh$ , where B is the area

V = 192 yd^3 $\displaystyle ;V = \frac{1}{3} Bh$ where B is the area
B = 64 yd^2

=> $\displaystyle V = \frac{1}{3} Bh$

=> $\displaystyle 192 \ yd^3 = \frac{1}{3} 64 \ yd^2 *h$

=> $\displaystyle h = 3*192 \ yd^3 / (64 \ yd^2) = 9 \ yd$

Rapha

I thank you.
• Nov 21st 2008, 06:41 PM
magentarita
ok...............
Quote:

Originally Posted by David24
By defintion, the volume of a square based pyramid is given by

Vol = (1/3) x Perpendicular Height x Area of Base

Subbing in the known parameters yields

192 = (1/3) x Perpendicular Height x 64

Thus,

the Perpendicular Height = (3 x 192) / 64

Hope this helps,

Regards,

David

I thank you.