Question 65

A cone is 32 cm high and the radius of its base is 8 cm. It is melted and recast into a sphere. Find the radius of the sphere

Solution

Volume of cone = Volume of sphere

Volume of cone= $$ \frac{1}{3} \times \frac{22}{7} \times r^2 \times h $$

Volume of sphere=$$ \frac{4}{3} \times \frac{22}{7} \times r^3 $$

$$ \frac{1}{3} \times \frac{22}{7} \times 8^2 \times 32 = \frac{4}{3} \times \frac{22}{7} \times r^3 $$

On solving we get $$r^3=512$$

r=8cm

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