A cone and a sphere have equal volumes. If the cone's height is twice its radius, what is the ratio of the cone's radius to the sphere's radius?
\(\sqrt[3]{{2}} : 1\)
Let cone radius = \(r\), cone height = \(2r\), sphere radius = \(R\).
\(\dfrac{{1}}{{3}}\pi r^2(2r) = \dfrac{{4}}{{3}}\pi R^3\)
\(\dfrac{{2}}{{3}}r^3 = \dfrac{{4}}{{3}}R^3\)
\(r^3 = 2R^3 \Rightarrow \dfrac{{r}}{{R}} = \sqrt[3]{{2}}\)
Hence \(r : R = \mathbf{{\sqrt[3]{{2}} : 1}}\)
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Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
