Ex.l. The volumes of a sphere and a...
Question

# Ex.l. The volumes of a sphere and a right circular cylinder having the same radius are equal , The ratio of the diameter of the sphere to the height of the cylinder is (1) 3:2 (2) 2:3 (3) 1:2 (4) 2:1

11th - 12th Class
Maths
Solution
68
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Sol. (1) Volume of sphere ( =frac{4}{3} pi r^{3} ) Volume of cylinder ( =pi r^{2} h ) According to the question, ( pi r^{2} h=frac{4}{3} pi r^{3} Rightarrow h=frac{4}{3} r ) ( Rightarrow frac{h}{r}=frac{4}{3} Rightarrow frac{h}{2 r}=frac{4}{3 times 2}=frac{2}{3} ) ( Rightarrow frac{d}{h}=frac{3}{2}, ) where ( d=2 r )