A copper wire 36 m long with a diameter of 2 mm is melted to make a sphere. Then the radius of the sphere is ______.
3 cm
The wire is a cylinder; on melting, its volume equals the volume of the sphere.
Radius of wire = 2 mm ÷ 2 = 1 mm = 0.1 cm
Length of wire = 36 m = 3600 cm
Volume of wire = π × (0.1)² × 3600
= 36π cm³
Volume of sphere = (4/3)πr³ = 36π
r³ = 36 × 3/4 = 27
r = 3 cm
Hence, 3 cm.
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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:
