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

Answer:

$336\text{ cm}^3$

Step-by-step 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 $=\text{side}\times\text{side}=12\times12\text{ cm}^2$

                                  $=144\text{ cm}^2$

Volume of pyramid $=\frac{1}{3}\times\text{base area}\times\text{height}$

putting values

                        $=\frac{1}{3}\times144\times8$

                        $=384\text{ cm}^3$

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

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

area of square base $=6\times6=36\text{ cm}^2$

Volume of small pyramid $=\frac{1}{3}\times36\times4$

                                          $=48\text{ cm}^3$

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 $336\text{ cm}^3$