A square pyramid and a cube have the same volume if the length of each side of the base of the square pyramid is 2 cm in the height of the cube is 4 cm what is the height of the pyramid

a 8cm

b 16cm

c 24cm

d 48 cm

Vol sq. pyramid = 1/3*s^2*h

Vol cube = s^3

since height of cube is 4, that height = s

V = (4) ^3 = 64 cubic cm

now since their Vs are the same,

1/3*s^2*h = 64

they said length of side in square pyramid

was 2, then:

1/3 * (2) ^2*h = 64

1/3*4*h = 64

4/3 h = 64

h = 64*3/4 = 16*3 = 48 cm

D) is the correct answer