A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. The area of the canvas required for the tent is :
Options:
A . 1300 m2
B . 1310 m2
C . 1320 m2
D . 1330 m2
Answer: Option C Radius, r = 12 m Height of conical part, h = (16 - 11) m = 5 m Slant height of conical part, $$\eqalign{ & l = \sqrt {{r^2} + {h^2}} \cr & \,\,\,\, = \sqrt {{{\left( {12} \right)}^2} + {{\left( 5 \right)}^2}} \cr & \,\,\,\, = \sqrt {169} \cr & \,\,\,\, = 13\,m \cr} $$ Height of cylindrical part, H = 11 m Area of canvas required : = Curved surface area of cylinder + Curved surface area of cone$$\eqalign{ & = 2\pi rH + \pi rl \cr & = \left[ {\frac{{22}}{7}\left( {2 \times 12 \times 11 + 12 \times 13} \right)} \right]{{\text{m}}^2} \cr & = \left[ {\frac{{22}}{7}\left( {264 + 156} \right)} \right]{{\text{m}}^2} \cr & = \left( {\frac{{22}}{7} \times 420} \right){{\text{m}}^2} \cr & = 1320\,{{\text{m}}^2} \cr} $$
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