10. What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 14 cm?

Question

pls help!! I'm behind and I don't understand. I would just like to know how to solve it please?

Answer 1

You would want the base of the square pyramid to fit exactly on
the base of the cube, and since the volume of the pyramid now
depends only on its height, make the height 14.

Max volume of pyramid = (1/3)(base)(height)
= (1/3)(14)^2 (14)
= (1/3)(14^3) = 2744/3 cm^3

btw, it really doesn't matter where the vertex of the pyramid is, as
long as it is 14 cm above the base, the volume would always be the same.

Answer 2

the base of the pyramid is the face of the cube ... 14 cm on a side

the height of the pyramid is the side length of the cube ... also 14 cm

volume of pyramid = 1/3 * base area * height

Answer 3

thankyou so much!!!