Multiple choice

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

  1. $ 1.063487 $
  2. $ 0.63487 $
  3. $ 0.063487 $

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of hemisphere = (2/3) * pi * r^3. Outer radius R = 1m + 0.01m = 1.01m. Inner radius r = 1m. Volume of iron = (2/3) * pi * (1.01^3 - 1^3) = (2/3) * 3.14159 * (1.030301 - 1) = (2/3) * 3.14159 * 0.030301 = 0.063487 cubic meters.

AI explanation

The iron used to make the hemispherical tank forms a hollow hemisphere with an inner radius of 1 m (100 cm) and an outer radius of 101 cm due to the 1 cm thickness. The volume of the iron is the difference between the outer and inner volumes, calculated using the formula (2/3) * pi * (R^3 - r^3). This gives (2/3) * (22/7) * (101^3 - 100^3), which equals (2/3) * (22/7) * 30301 = 636421 / 6300. Performing the division results in 0.063487 cubic meters.

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