Question

What is the maximum volume of a square pyramid that can fit inside a cube with edges 18 cm long?

A.
5832 cm3

B.
2916 cm3

C.
1944 cm3

D.
972 cm3

Answer 1

The correct answer is C. 1944 cm³

Explanation:

We are given a cube.

Edge length of a cube = 18 cm

We need to find the maximum volume of a square pyramid that can fit inside the given cube of edge length 18 cm

⇒ Side length of pyramid = Edge length of cube = 18 cm

So, Maximum volume of the square pyramid = Volume of the pyramid with side length of 18 cm

`\text{Maximum volume of the square pyramid = }(1)/(3)* 18* 18* 18`

⇒ Maximum volume of the square pyramid = 1944 cm³

Hence, The correct answer is C. 1944 cm³

Answer 2

we know that
[volume of a square pyramid]=(1/3)*b²*h
b--------> is the length side of the cube-------> 18 cm
h-----> is the height of the cube-------> 18 cm

[volume of a square pyramid]=(1/3)*18²*18----> 1944 cm³

the answer is
1944 cm³