Question

PLEASE HELP 33 POINTS AND I WILL MARK BRAINLIEST!!!!!!!! THANKS!!!!!!!!!!!

Sarah has two similar regular pyramids with pentagon-shaped bases. The smaller has a scale factor of 2:3 when compared to the larger. Only the smaller pyramid is shown.

She calculates the area of the base of the pyramid (through long, hard work) to be 220.22 square units. The height of the pyramid is 9 units. Now she needs to calculate the volume of the pyramid.

(a) Calculate the volume of the pyramid for Sarah.

(b) "Oh, no!" Sarah exclaims. "Now I have to go through all this hard work again to find the volume of the larger pyramid!" Does she? Explain.

(c) Calculate the volume of the larger pyramid for Sarah.

Answer 1

(a) Volume of any Pyramid =   $\frac{1}{3} * (Base-Area)*height = \frac{1}{3} *220.22*9 = 660.66$ cubic units

(b) Sarah doesn't have to go through all the hard work as the smaller pyramid has a ratio of 2:3 to the bigger pyramid, so we get the equation, to help us solve it.

$660.66 = \frac{2}{3} *(Area-of-larger-pyramid)$

Hope that helps!