Question:
The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.
Solution:
The slant height of the frustum of a cone is l=10cm. The radii of the upper and lower circles of the bucket are r1 =33cm and r2 =27cm respectively.
The total surface area of the frustum of the cone is
$S_{1}=\pi\left(r_{1}+r_{2}\right) \times l+\pi r_{1}^{2}+\pi r_{2}^{2}$
$=\pi \times(33+27) \times 10+\pi \times 33^{2}+\pi \times 27^{2}$
$=600 \pi+1089 \pi+729 \pi$
$=7599.42 \mathrm{~cm}^{2}$
Hence total surface area is $7599.42 \mathrm{~cm}^{2}$