Question

A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.

Answer 1

The radii of the bottom and top circles are r₁ = 10 cm and r₂ = 6 cm respectively. The height of the frustum cone is h= 3 cm. Therefore, the volume of the bucket is

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

`=1/3pi(10^2+10xx6+6^2)xx3`

= 616 cm³

Hence Volume = 616 cm³

The slant height of the bucket is

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

`=sqrt((10-6)^2+3^2)`

`=sqrt(25)`

= 5cm

The total surface area of the frustum cone is

`pi(r_1+r_2)xxl+pir_1_pir_2^2`

`=22/7xx(10+6)xx5+22/7xx10^2+22/7xx6^2`

`=4752/7`Square cm

= 678.85 Square cm

Hence Total surface area = 678.85