Question 63

If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

Solution

Radius of cylinder, $$R = 7$$ cm and height of cylinder, $$H = 9$$ cm

Let height of cone = $$h$$ cm and radius of cone, $$r = 7$$ cm

According to ques, volume of cone = volume of cylinder

=> $$\frac{1}{3} \pi r^2 h = \pi R^2 H$$

=> $$\frac{1}{3} \times (7)^2 \times h = (7)^2 \times 9$$

=> $$h = 9 \times 3 = 27$$ cm

=> Ans - (C)

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