Question

A shuttle used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere as shown in the figure. The external diameters of the frustum are 6 cm and 2 cm; and the height of the entire shuttle is 7 cm. Find its external surface area.

Answer 1

$r = 3cm \: and \: 1cm$
external surface area is curved syrface area
$csa = \pi(r1 + r2)l$
slant height is
$\sqrt{ {h}^{2} + {(r1 - r2)}^{2} }$
slant height is
$\sqrt{ {7}^{2} + {2}^{2} } = \sqrt{49 + 4} = \sqrt{53} \: \: \\ now \: csa = \frac{22}{7} (3 + 1) \sqrt{5 3} \\ = \\ \frac{22}{7 } \times 4 \times \sqrt{53 } = 12.57 \sqrt{53}$