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A joker's cap is in the form of a right circular cone whose base radius is 7 cm and height is 24 cm. Find the area of the sheet required to make 10 such caps.

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5500 {cm}^{2}

5300 {cm}^{2}

5200 {cm}^{2}

5000 {cm}^{2}

answer is A.

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Detailed Solution

Given Radius of cone base,

r = 7 cm

Height of cone,

h = 24 m

Suppose slant height =

l

Now, we have,

l^{2} = h^{2} + r^{2}

l^{2} = 24^{2} + 7^{2}

l^{2} = 576 + 49

l^{2} = 625

l = \sqrt{625}

l = 25 cm

Now, curved surface area of the cap of joker

A_{cs} = πrl

A_{cs} = \frac{22}{7} \times 7 \times 25

A_{cs} = 22 \times 25

A_{cs} = 550 {cm}^{2}

For 10 jokers cap curved surface area,

= 10 \times 550

= 5500 {cm}^{2}

Thus, the correct option is 1.

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