Question 70

The diameter of a sphere is twice the diameter of another sphere. The curved surface area of the first and the volume of the second are numerically equal. The numerical value of the radius of the first sphere is

Solution

Let radius of first sphere = $$2r$$ cm

=> Radius of second sphere = $$r$$ cm

Also, curved surface area of the first and the volume of the second are equal

=> $$4\pi (2r)^2=\frac{4}{3}\pi r^3$$

=> $$4r^2=\frac{r^3}{3}$$

=> $$r=4 \times 3=12$$ cm

$$\therefore$$ Radius of the first sphere = $$2 \times 12=24$$ cm

=> Ans - (B)

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