Find the volume of a cylinder whose height is 21 cm and its radius is \(\tfrac{3}{5}\) of the radius of another cylinder with a volume of 317900 cm3 and a height of 14 cm. (Use \(\pi = \tfrac{22}{7}\))
171666 cm3
Volume of the second cylinder: \(V = \pi r^2 h = 317900\), with h = 14 cm.
So \(r^2 = \dfrac{317900}{\frac{22}{7}\times14} = \dfrac{317900}{44} = 7225\), giving \(r = 85\) cm.
The first cylinder's radius is \(\tfrac{3}{5}\) of 85, i.e. \(51\) cm, with height 21 cm.
Its volume: \(\tfrac{22}{7}\times51^2\times21 = \tfrac{22}{7}\times2601\times21 = 171666\) cm3.
Hence, the volume of the cylinder is 171666 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:
