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Question

A right angle triangle of base 4 cm and height 3 cm is rotated about its height. The curved surface area and volume of the solid obtained are _____ (in cm2) and _____ (in cm3) respectively.


A
18π & 14π
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B
20π & 16π
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C
16π & 18π
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D
22π & 20π
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Solution

The correct option is B 20π & 16π
As we rotate a right angle triangle about its height we get a cone.
Its radius = r = Base of the triangle = 4 cm
and, height = h= 3 cm

By Pythagoras' theorem;
Hypotenuse =base2+height2 =42+32 =5 cm

Slant height of cone, l= Hypotenuse = 5 cm

Curved surface area of the cone
=πrl =π×4×5 =20π cm2

Volume of the cone
=13πr2h =13×π×16×3 =16π cm3

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