question_answer

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. What is the area of the curved surface for conical portion?

A) \[\frac{3434}{9}{{m}^{2}}\]               

B) \[\frac{3431}{8}{{m}^{2}}\]

C) \[\frac{3432}{7}{{m}^{2}}\]               

D) \[\frac{3234}{7}{{m}^{2}}\]

Correct Answer: C

Solution :

Slant height of cone = \[\sqrt{{{5}^{2}}+{{12}^{2}}}\](by Pythagoras theorem) =  \[\sqrt{25+144}=\sqrt{169}=13\,\,m\] Curved surface area for conical portion =   \[\pi rI\] \[\frac{22}{7}\times 12\times 13=\frac{\mathbf{3432}}{\mathbf{7}}\mathbf{sq}.\mathbf{m}.\]