Question 12 Marks
A sphere and a cone have the same radii. If their volumes are also equal, prove that the height of the cone is twice its radius.
Answer
View full question & answer→Let $r$ be the radii of sphere and cone.
Volume of sphere $=\frac{4}{3} \pi r^3=\frac{1}{3} \pi r^2 h \quad( h =2 r$ for sphere $)$
Volume of cone $=\frac{1}{3} \pi r^2 h$
But $h=2 r$ for sphere
Therefore,$h=2 r$ for cone also.
Hence, proved
Volume of sphere $=\frac{4}{3} \pi r^3=\frac{1}{3} \pi r^2 h \quad( h =2 r$ for sphere $)$
Volume of cone $=\frac{1}{3} \pi r^2 h$
But $h=2 r$ for sphere
Therefore,$h=2 r$ for cone also.
Hence, proved