1. A sphere and cube have equal surface areas. The ratio of the volume of the sphere to that of the cube is
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By: anil on 05 May 2019 02.25 am
Let radius of sphere = $$r$$ and side of cube = $$a$$ units According to ques, Surface area of sphere = Surface area of cube => $$4pi r^2=6a^2$$ => $$frac{r^2}{a^2}=frac{3}{2pi}$$ => $$(frac{r}{a})^3=(frac{3}{2pi})^{frac{3}{2}}$$ $$ herefore$$ Volume of sphere : Volume of cube = $$frac{frac{4}{3}pi r^3}{a^3}=(frac{4pi}{3})(frac{r}{a})^3$$ = $$frac{2^2pi}{3}(frac{3}{2pi})^{frac{3}{2}}$$ = $$frac{(2)^{2-frac{3}{2}}(3)^{frac{3}{2}-1}}{(pi)^{frac{3}{2}-1}}$$ = $$frac{(2)^{frac{1}{2}}(3)^{frac{1}{2}}}{(pi)^{frac{1}{2}}}$$ = $$sqrt{6}:sqrt{pi}$$ => Ans - (B)
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