Sourav’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 2 dozen caps.

1. 23100 cm

^{2}

2. 26400 cm

^{2}

3.

13200 cm^{2}

4. 46200 cm

^{2}

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Correct Answer – Option 3 :

13200 cm

^{2}Given:Radius of conical cap = 7 cm

Height of conical cap = 24 cm

Formula used:Curved surface area of cone = πrl

l

^{2}= r^{2}+ h^{2 }Where, r = radius of cone

l = slant height of cone

h = height of cone

Calculation:l

^{2}= 7^{2}+ 24^{2 }⇒ l

^{2}= 49 + 576 = 625⇒ l = √625 = 25 cm

Curved surface area of cone = π × 7 × 25 = 550 cm

^{2}Area of sheet for 2 dozen caps = 550 × 2 × 12 = 13200 cm

^{2}∴The area of the sheet required to make 2 dozen caps is 13200 cm^{2}