Question

A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. 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. $226285.714m^3,15085.714m^2$
• D. $5657.14m^3,13828.57m^2$

Answer 1

The correct option is C $226285.714m^3,15085.714m^2$

Height of tent = Height of cylinder + Height of cone
Given: Height of the cone (h) = 30 m
Height of the cylinder (H) = 65 - 30 = 35 m
Radius of the cylinder = Radius of the cone = 40 m


Volume of the circus tent = Volume of cylinder + Volume of cone
$=\pi r^{2}H+\frac{\pi r^{2}h}{3}=\pi r^2(H+\frac{h}{3})=\frac{22}{7}\times (40{)}^2\times (35+\frac{30}{3})=\frac{22}{7}\times 1600\times (35+10)=\frac{22}{7}\times 1600\times 45=226285.714m^3\text{Slant height of the cone},l=\sqrt{h^2+r^2}=\sqrt{{30}^2+{40}^2}=50m$

Now, area of cloth required in making the tent
= Curved surface area of cylinder + Curved surface area of cone
$=2\pi rH+\pi rl=\pi r(2H+l)=\frac{22}{7}\times 40(70+50)=\frac{22}{7}\times 40\times 120=15085.714m^2$