A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent.
(Take : π = 22/7)
The height of the frustum cone is h = 8 m. The radii of the end circles of the frustum are r1 = 13m and r2 =7m.
The slant height of the frustum cone is
$l=\sqrt{\left(r_{1}-r_{2}\right)^{2}+h^{2}}$
$=\sqrt{(13-7)^{2}+8^{2}}$
$=\sqrt{100}$
$=10$ meter
The curved surface area of the frustum is
$S_{1}=\pi\left(r_{1}+r_{2}\right) \times l$
$=\pi \times(13+7) \times 10$
$=\pi \times 20 \times 10$
$=200 \pi \mathrm{m}^{2}$
The base-radius of the upper cap cone is 7m and the slant height is 12m. Therefore, the curved surface area of the upper cap cone is
$S_{2}=\pi \times 7 \times 12$
$=\frac{22}{7} \times 7 \times 12$
$=22 \times 12$
$=264 \mathrm{~m}^{2}$
Hence, the total canvas required for the tent is
$S_{1}+S_{2}=200 \pi+264$
$=892.57 \mathrm{~m}^{2}$
Hence total canvas is $892.57 \mathrm{~m}^{2}$