Question
The outer radius of a spherical shell is 8 cm, and the
thickness of the shell is 2 cm. Find the volume of the metal used for the shell (in cubic cm). (Use π = 22/7)Solution
Given: Outer radius (R) = 8 cm Thickness of shell = 2 cm So, inner radius (r) = 8 − 2 = 6 cm Volume of metal used = Volume of outer sphere − Volume of inner sphere Formula for volume of a sphere: V = (4/3) × π × r³ So, Volume of metal = (4/3) × π × (R³ − r³) = (4/3) × (22/7) × (8³ − 6³) = (4/3) × (22/7) × (512 − 216) = (4/3) × (22/7) × 296 Now calculate: 4 × 22 × 296 = 26048 So, Volume = 26048 / 21 cubic cm ≈ 1240.38 cubic cm³
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