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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