Question

In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.

• A. 24π cm
• B. 52π cm
• C. 26π cm
• D. 72π cm

Answer 1

The correct option is C

26π cm

As cap is of conical shape,
area of paper
= curved surface area of cap

Slant height $=\sqrt{\left(b^2\right)+\left(h^2\right)}$

$=\sqrt{\left({24}^2\right)+\left({10}^2\right)}$

$=26cm$

Curved surface area of cap = $\pi$rl

C.S.A. = $\pi$ $\times$ 24 $\times$ 26

C.S.A = 624$\pi$ $c{m}^2$

Therefore,
area of paper required = 624$\pi$ $c{m}^2$

Area of rectangle = Length $\times$ Breadth
= 24 $\times$ b

Since, 24 $\times$ b = 624$\pi$ ; b = 26$\pi$ cm