The curved surface area of a right circular cone is 1000 cm² and its radius is 10 cm. What is its volume? (in cm³)
3164.43
Curved surface area of a cone = πrl; volume = (1/3)πr²h, where l² = r² + h².
πrl = 1000 ⇒ l = 1000/(22/7 × 10) = 350/11 = 31.82 cm
h² = l² - r² = 1012.40 - 100 = 912.40 ⇒ h = 30.21 cm
Volume = (1/3) × 22/7 × 10² × 30.21 = 3164.43 cm³ (approximately)
Hence, 3164.43.
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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:
