A perfect cube with a side length of 8 cm has the largest possible sphere fitted inside it. What is the volume of the empty space within the cube?
512 - 256π/3 cm^3
The volume of the cube with side 8 cm is \(V_{cube} = 8^3 = 512\) cm³.
The largest sphere that fits inside the cube has a diameter equal to the cube's side, so its radius is \(r = \frac{8}{2} = 4\) cm.
The volume of this sphere is \(V_{sphere} = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (4)^3 = \frac{4}{3}\pi \times 64 = \frac{256\pi}{3}\) cm³.
The empty space is \(V_{cube} - V_{sphere} = 512 - \frac{256\pi}{3}\) cm³.
Hence, the answer is 512 - 256π/3 cm³.
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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:
