question_answer

A tent is to be built in the form of a cylinder of radius 10 metre surmounted by a cone of the same radius. If the height of the cylindrical part is 5 metre and slant height of the conical part is 15 metre, how much canvas will be required to build the tent? Allow 20% extra canvas for folding and stitching. \[\left( \text{Take}\,\pi =\frac{22}{7} \right)\]

A)  714.43 sq. metre

B)  772.14 sq. metre

C)  783.86 sq. metre

D)  942.85 sq. metre

Correct Answer: D

Solution :

Curved surface area of cylindrical part \[=2\pi rh\] \[=2\times \frac{22}{7}\times 10\times 5\] \[=\frac{2200}{7}\]sq. metre Curved surface area of conical part \[=\pi rt\] \[=\frac{22}{7}\times 10\times 15\] \[=\frac{3300}{7}\]sq. metre Total curved surface area \[=\left( \frac{2200}{7}+\frac{3300}{7} \right)\,\text{sq}\text{.}\,\text{metre}\] \[\therefore \]Area of required canvas \[=\left( \frac{5500}{7}\times \frac{120}{100} \right)\,\text{sq}\text{.}\,\text{metre}\] = 942.85 sq. metre