Question

A square pyramid is placed inside a cube having a volume of 729 in3. The pyramid has the same height as the cube and the base of the pyramid is one face of the cube. Which is the ratio of the volume of the pyramid to the volume of the cube?

a 1/9
b 1/2
c 1/3
d 2/3

Answer 1

1/3

Explanation:

pyramid height = cube height , a = h (GIVEN)

`so, v= (1)/(3) * a^(2) * h = (1)/(3) * a^(3)\\a = \sqrt[3]{3v} = \sqrt[3]{3*729} = 13 in\\\\cube volume = a^(3) = 13^(3) = 2187 in^(3) \\\\ratio = (729)/(2187)= (1)/(3) (ANS)`

Answer 2

I really don’t know but I hope you find the correct answer