# A tent is in the form of a right circular cylinder surmounted by a cone.

Question:

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.

Solution:

It is given that

Diameter of cylinder = 24 m

= 24/2 = 12 cm

Also radius of cone = 12 m

Height of cylinder = 11 m

Height of cone = 16 - 11 = 5 m

Slant height of cone

$=\sqrt{5^{2}+12^{2}}$

= 13 m

Therefore area of canvas required for the tent = πrl + 2πrh

= 22/7 [(12 ∗ 13) + (2 ∗ 12 ∗ 11)] = 490.286 + 829.714

$=1320 \mathrm{~m}^{2}$