Question

A circus tent consists of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40m. The total height of the tent is 65m and that of the height of the cone is 30m. Find the volume of the tent and the area of the cloth used for making it.

• A. $5658.63m^3,13835.57m^2$
• B. $5325.42m^3,14251.57m^2$
• C. $6354.36m^3,13921.46m^2$
• D. $5657.14m^3,13828.57m^2$

Answer 1

The correct option is D $5657.14m^3,13828.57m^2$

Height of tent = height of cylinder + height of cone
Given height of cone(h) = 30m
Height of the cylinder(H) = 65 - 30 =35m
Radius of the cylinder = radius of the cone = 40m
Volume of the circus tent = Volume of cylinder + volume of cone
$=\pi r^{2}H+\frac{\left(\pi r^{2}h\right)}{3}=\pi r^2(H+\frac{h}{3})[where,H=heightofcylinderand,h=heightofcone]=\frac{22}{7}\times {40}^2\times (35+\frac{30}{3})=226,285.714m^{3}Slantheightofthecone=\sqrt{h^2+r^2}=\sqrt{{30}^2+{40}^2}=50m$
Now, Area of cloth required in making the tent
= Curved surface area of cylinder + Curved surface area of cone
$=2\pi rh+\pi rl=\pi r(2h+l)=\frac{22}{7}\times 40(70+50)=15,085.71m^2$