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Mathematics

A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.

Mensuration

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Answer

Given,

Circumference = 198 cm

∴ 2πr = 198

⇒ r = 1982π=1982×227=198×744=138644\dfrac{198}{2π} = \dfrac{198}{2 \times \dfrac{22}{7}} = \dfrac{198 \times 7}{44} = \dfrac{1386}{44} = 31.5 cm.

By formula,

Capacity of bowl=23πr3=23×227×(31.5)3=2×22×31255.87521=1375258.521=65488.5 cm3.\text{Capacity of bowl} = \dfrac{2}{3}πr^3 \\[1em] = \dfrac{2}{3} \times \dfrac{22}{7} \times (31.5)^3 \\[1em] = \dfrac{2 \times 22 \times 31255.875}{21} \\[1em] = \dfrac{1375258.5}{21} \\[1em] = 65488.5 \text{ cm}^3.

Hence, capacity of bowl = 65488.5 cm3.

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