The length of each edge of a cube is 10 cm. If a sphere is inscribed inside the cube, what is the ratio of the surface area of the sphere to the outer surface area of the cube?
\(\pi : 6\)
A sphere inscribed in a cube touches all its faces, so the sphere's diameter equals the cube's edge, \(10\) cm, giving radius \(r = 5\) cm.
The surface area of the sphere is \(4\pi r^2 = 4\pi (5)^2 = 100\pi\) cm2.
The outer surface area of the cube is \(6a^2 = 6 (10)^2 = 600\) cm2.
The required ratio is \(\frac{100\pi}{600} = \frac{\pi}{6}\), that is \(\pi : 6\).
Hence, the ratio of the sphere's surface area to the cube's surface area is \(\pi : 6\).
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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 = \(22\over7\)]
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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:
