#### Question

The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

#### Solution

The height of the frustum cone is h= 12 cm. The radii of the bottom and top circles are r_{1} = 12cm and r_{2} = 3cm respectively.

The slant height of the frustum cone is

`l=sqrt((r_1-r_2)^2+h^2`

`=sqrt((12-3)^2+12^2`

`=sqrt(225)`

= 15 cm

The total surface area of the frustum cone is

`=pi(r_1+r_2)xxl+pir_2^2+pir_2^2`

`=pixx(12+3)xx15+pixx12^2+pixx3^2`

= π x 225 x 26 + 144π + 9π

= 378π cm^{2}

Hence Total surface area = 378π cm^{2}

The volume of the frustum cone is

`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`

`=1/3pi(12^2+12xx3+3^2)xx12`

`=1/3xxpixx189xx12`

= 756π cm^{3}

Hence Volume of frustum = 756π cm^{3}