Multiple choice

Find the quantity of water in litres in a hemispherical bowl of radius $21cm$. The bowl is completely filled with water. (Take $\pi=\cfrac{22}{7}$)

  1. $19.404$ litres
  2. $16.141$ litres
  3. $22.254$ litres
  4. $18.204$ litres
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A Correct answer
Explanation

Volume of a hemisphere = (2/3) * pi * r^3. With r = 21 and pi = 22/7, V = (2/3) * (22/7) * 21^3 = (2/3) * (22/7) * 9261 = 2 * 22 * 441 = 19404 cm^3. Since 1000 cm^3 = 1 litre, this is 19.404 litres.

AI explanation

The volume of a hemisphere is found using the formula two thirds multiplied by pi multiplied by the radius cubed. Substituting the given radius gives two thirds multiplied by 22 divided by 7 multiplied by 21 cubed, which simplifies to 19404 cubic centimeters. Since one liter equals 1000 cubic centimeters, dividing 19404 by 1000 gives the quantity of water as 19.404 liters.

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