Question

A tent is in the shape of a cone surmounted on the top of a cylinder. Height of the cone is half that of the cylinder and the base radius of the cylinder is 3m.if the canvas required for the tent is 198 m^2 ,then the total height of the tent is

Answer 1

$\huge\mathbb{A~N~S~W~E~R}$

From question cone is surmounted on the top of cylinder therefore radius of cone and cylinder are same.

Canvas required 198m^2 and on base canvas is not required.

Canvas is only for curved surface area of cone.

$198 = \pi \times r \times l \\ \\ 198 = \frac{22}{7} \times 3 \times l \\ \\ \frac{198 \times 7}{22 \times 3} = l \\ \\ \\ l = 21 \: m$

In most of case cone is right circular cone.

$h = \sqrt{ {l}^{2} - {r}^{2} } \\ \\ h = \sqrt{ {21}^{2} - {3}^{2} } \\ \\ h = \sqrt{432} \\ \\ h = 20.78 \: m$

${\huge\color{Red}{Answer~is~20.78m }}$

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