Question

Two square pyramids have the same volume. For the first pyramid , the side length of the base is 14 inches, and the height is 24 inches. The second pyramid has a height of 96 inches. What is the side length of the base of the second pyramid.

Answer 1

set up 2 volume equations

Answer 2

Volume = side length^2 * height * (1/3)

so

(14)(14)(24)(1/3) = (96)(1/3)x^2

Answer 3

then the 1/3's cancel out

(14)(14)(24) = 96x^2

solve for x

Answer 4

4704=9216x

Answer 5

nope not quite

Answer 6

the ^2 only applies to the x

so

4704 = 96x^2

now solve for x

Answer 7

48?

Answer 8

nope

what's 4704/96?

Answer 9

49

Answer 10

good. now what's the square root of 49?

Answer 11

7

Answer 12

good, that's your final answer