Aspire Faculty ID #15399 · Topic: MAH MCA CET 2023 · Just now
MAH MCA CET 2023

A cone of base radius $1$ and height $15,m$ is melted to form a sphere of equal radius. Find radius nearer to:

Solution

Volume of cone $= \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3}\pi(1)^2(15)=5\pi$. Let sphere radius $= R$, then $\dfrac{4}{3}\pi R^3 = 5\pi \Rightarrow R^3 = \dfrac{15}{4} \Rightarrow R \approx 0.5$.

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