Question

A circus tent is in the form of a cone over a cylinder. The diameter of the base is $9$ m, the height of cylindrical part is $4.8$ m and the total height of the tent is $10.8$ m. The canvas required for the tent is ..........

• A. $24.184$ sq.m
• B. $2418.4$ sq.m
• C. $241.84$ sq.m
• D. None of these

Answer 1

The correct option is C $241.84$ sq.m

The amount of canvas used to make the tent $=$ Curved surface area of cylindrical part $+$ Curved surface area of the conical part.
Curved Surface Area of a Cylinder of Radius "$R$" and height "$h$" $=2\pi Rh$
Radius of the cylindrical part $=\frac{Diameter}{2}=\frac{9}{2}$ 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 $=\frac{Diameter}{2}=\frac{9}{2}m$

Height of the conical part $=10.8-4.8=6$ m

For a cone, $l=\sqrt{h^2+r^2}$, where $h$ is the height.

Hence, $l=\sqrt{6^2+{4.5}^2}$

$\therefore l=7.5$ m

Hence, area of canvas $=2\times \pi \times 4.5\times 4.8+\pi \times 4.5\times 7.5$

$=76.95\pi$

$=241.84m^2$