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A metallic hemispherical bowl is made up of steel. The total steel used in making the bowl is 342π cm3. The bowl can hold 144π cm3 water. What is the thickness (in cm) of bowl and the curved surface area (in cm2) of outer side?

A metallic hemispherical bowl is made up of steel. The total steel used in making the bowl is 342π cm3. The bowl can hold 144π cm3 water. What is the thickness (in cm) of bowl and the curved surface area (in cm2) of outer side? Correct Answer 3, 162π

Inner volume of the hemispherical bowl = 144π cm3

⇒ 2/3πr3 = 144π

⇒ r = 6 cm

Material used in hemispherical bowl = 342π cm3

⇒ 2/3π(R3 - r3) =342π

⇒ (R3 - r3) = 513

Since r = 6 cm

⇒ R3 = 513 + 216 = 729

⇒ R = 9 cm

∴ Thickness of the bowl = R - r = 9 - 6 = 3 cm

∴ Curved surface area of outer side = 2πR2

⇒ 2 × π × 81 = 162π cm2

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