A solid hemisphere has radius 14 cm. It is melted to form a cylinder such that the ratio of its curved surface area and total surface area… — Answer & Discussion

A solid hemisphere has radius 14 cm. It is melted to form a cylinder such that the ratio of its curved surface area and total surface area is 2 : 3. What is the radius (in cm) of its base?

A$\frac{{10}}{{\sqrt[3]{3}}}$
B$\frac{{14}}{{\sqrt[3]{3}}}$
C$\frac{7}{{\sqrt[3]{3}}}$
D$\frac{{21}}{{\sqrt[3]{3}}}$

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CCommunity22 Apr 2019

According to question,

Curved surface area of cylinder/Total surface area of cylinder = 2/3

⇒ 2πRh/2πR(R + h) = 2/3

⇒ h/ (R + h) = 2/3

⇒ 3h = 2R + 2h

⇒ h = 2R ---- (1)

? Volume of cylinder = Volume of solid hemisphere

⇒ πR2h = 2/3πr3 (where, R = radius of cylinder and r = radius of solid hemisphere)

Putting value of ‘h’ from equation (1),

⇒ R2 × 2R = (2/3) × 14 × 14 × 14

⇒ R3 = (14 × 14 × 14)/3

⇒ R = 14/?3

∴ Radius of its base = 14/?3 cm

CCommunity06 Jul 2021

$=14/ \sqrt{3} $