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Q.

A right angled triangle whose sides are3 cm, 4 cm and 5 cmrevolved about the sides containing the right angle in two ways. Find the difference in volumes of the two cones so formed.

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a

4 π {cm}^{3}

b

4 π {cm}^{3}

c

4 π {cm}^{3}

d

4 π {cm}^{3}

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Detailed Solution

Given,
The sides of right angle = 3, 4, and 5 cm
Here, hypotenuse side is 5 cm (longest side).
So, sides containing right angles are 3 cm and 4 cm.
Now, the triangle is revolve around 3 cm and 4 cm. Here, we get two cones of this revolution with 3 cm radius and 4 cm radius with height 4 cm and 3 cm respectively.
Thus, the volumes,

V_{1} = \frac{1}{3} π 3^{2} (4)

V_{1} = 12 π

Also,

V_{2} = \frac{1}{3} π 4^{2} (3)

V_{2} = 16 π

Thus, difference in the volume,

Δ V = π (16 - 12)

Δ V = 4 π {cm}^{3}

Hence, option 2 is correct.

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