Question

A square pyramid of height 6 inches has a volume of 405 cubic inches. If the volume of a similar square pyramid is 3240 cubic inches, what is its height?
6 inches

12 inches

14 inches

24 inches
Could you explain how to solve this? When I tried working this out I got 48.

Answer 1

@soulflower

Apply this theorem:

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

That gives the equation:

405/3240 = (6/h) ^3 where h is the height of the larger similar pyramid.

Solve the equation for h.

The answer is not 48.

Answer 2

@soulflower What did you get for h?

Answer 3

I multiplied 6 and 3240 then divided that by 405 and still got 48. I'm not sure what I'm doing wrong.

Answer 4

405/3240 = (6/h) ^3

405/3240 simplifies to 1/8 because 405*8 = 3240

So, the equation becomes:

1/8 = (6/h) ^3

(1/2)^3 = (6/h)^3

Take cube roots of both sides and see what you get. @soulflower

Answer 5

1/2 = 6/h

h = ? @soulflower

Answer 6

12 (: Thank you. I see where I went wrong.

Answer 7

12 is what I got, too.