Question

A conical tent with base-radius $7$ m and height $24$ m is made from $5$ m wide canvas. The length of the canvas used is $(\pi =\frac{22}{7})$:

• A. $100$ m
• B. $105$ m
• C. $110$ m
• D. $115$ m

Answer 1

The correct option is C $110$ m

Here, Area of the canvas $=$ Curved surface area of the conical tent.
Since the canvas is rectangular in shape, its area is $=$ length $\times$ width .
Curved surface area of a cone $=\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height.
For a cone, $l=\sqrt{h^2+r^2}$, where $l$ is the slant height.

Hence, $l=\sqrt{{24}^2+7^2}$

$\Rightarrow l=\sqrt{625}$

$\Rightarrow l=25$ cm

Hence, length $\times 5=\frac{22}{7}\times 7\times 25$

$\therefore$ length $=110$ m.

Therefore, option $C$ is correct.