## 123F 4 years ago The volume of a square based pyramid is 81 cubic meters. What is the volume of the cube with the same side length and height? A)9m3 B)27m3 C)243m3 D)729m3 moderator help

1. amistre64

the volume of the base?

2. amistre64

3. 123F

what

4. amistre64

The volume of "a square based pyramid" is 81 cubic meters. What is the volume of "the cube" with the same side length and height? thats better

5. 123F

thank you ;)

6. amistre64

the volume of any pointy shape is: (1/3) (base area) (height) to wit; 81 = (1/3) (base area) (h) ; multiply thru by 3 3(81) = s^2 * h ; s^2 refers to the square base area, divide out the h. 243/h = s^2 ; now square root each part sqrt(243/h) = s

7. 123F

so C)243m3

8. amistre64

hmmm, prolly still not reading it correctly; cube tends to mean a shape with sides and height being equal, but this might mean a cube like shape in general

9. amistre64

if height = side length we get sqrt(243/s) = s 243/s = s^2 243 = s^3 s = cbrt(243) .... might be a better interpretation but its hard to tell with the way it is written

10. amistre64

the volume would then be cbrt(243)^3 = 243m^3 which is prolly the right answer

11. 123F

so C)243m3