Question

A circus tent is cylindrical upto a height of 3 cm and conical above it. If the diameter of the base is 105 m and the slant height of the conical part is 53 m, find the total cost of the canvas used to make the tent when the cost per square metre of the canvas is Rs. 10. (Take $\pi =22/7$)

• A. Rs. 97350
• B. Rs. 97450
• C. Rs. 97550
• D. Rs. 97650

Answer 1

Answer: (A)

Rs. 97350

The amount of canvas used to make the tent $=$ Curved surface area of cylindrical part $+$ Curved surface area if the conical part.

Curved Surface Area of a Cylinder of Radius $"R"$ and height $"h"$ $=2\pi Rh$
Radius of the cylindrical part $=\frac{Diameter}{2}=\frac{105}{2}$ m

Curved surface area of a cone $=\pi rl$ where $r$ is the radius of the cone and $l$ is the slant height.

Radius of the conical part $=\frac{Diameter}{2}=\frac{105}{2}$

Hence, area of canvas = $2\pi rh+\pi rl$

$=2\times \frac{22}{7}\times \frac{105}{2}\times 3+\frac{22}{7}\times \frac{105}{2}\times 53=9735m^2$

Cost of canvas at $Rs10$ per sq m $=9735\times 10=Rs.97350$