Question

A wooden model of a square pyramid has a base edge of 12 cm and an altitude of 8 cm. A cut is made parallel to the base of the pyramid that separates it into two pieces: a smaller pyramid and a frustum. Each base edge of the smaller pyramid is 6 cm and its altitude is 4 cm. How many cubic centimeters are in the volume of the frustum

Answer 1

`336\text{ cm}^3`

Explanation:

GIVEN: A wooden model of a square pyramid has a base edge of
`12\text{ cm}` and an altitude of
`8\text{ cm}`. A cut is made parallel to the base of the pyramid that separates it into two pieces: a smaller pyramid and a frustum. Each base edge of the smaller pyramid is
`6\text{ cm}` and its altitude is
`4\text{ cm}`.

TO FIND: Volume of frustum.

SOLUTION:

Base edge of bigger square pyramid
`=12\text{ cm}`

Altitude of bigger square pyramid
`=8\text{ cm}`

area of square base
`=\text{side}*\text{side}=12*12\text{ cm}^2`

`=144\text{ cm}^2`

Volume of pyramid
`=(1)/(3)*\text{base area}*\text{height}`

putting values

`=(1)/(3)*144*8`

`=384\text{ cm}^3`

Base edge of smaller pyramid
`=6\text{ cm}`

Altitude of smaller pyramid
`=4\text{ cm}`

area of square base
`=6*6=36\text{ cm}^2`

Volume of small pyramid
`=(1)/(3)*36*4`

`=48\text{ cm}^3`

Volume of frustum
`=\text{Volume of bigger pyramid}-\text{volume of smaller pyramid}`

`=384-48`

`=336\text{ cm}^3`

Hence the volume of frustum is
`336\text{ cm}^3`