Question

A tent is in the form of a cylinder of diameter $8m$ and height $2m$, and surmounted by a cone of equal base and height $3m$. The canvas used for making the tent is equal to:

• A. $36\pi m^2$
• B. $28\pi m^2$
• C. $24\pi m^2$
• D. $38\pi m^2$

Answer 1

The correct option is A $36\pi m^2$

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 $=\frac{Diameter}{2}=4m$
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 $=\frac{Diameter}{2}=4m$

For a cone, $l=\sqrt{h^2+r^2}$,

where $h$ is the height

$l=\sqrt{3^2+4^2}m$

$l=5m$
Hence, area of canvas $=(2\times \pi \times 4\times 2)+(\pi \times 4\times 5)=36\pi m^2$