A hemispherical bowl is made of silver and has an inner diameter of 4 cm if the thickness of silver is 0.5 cm. Find the volume of silver used in making the bowl correct to two places of decimals (use π = 3.14).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 15.96 cm3.
Inner diameter = 4 cm, so the inner radius r = 4/2 = 2 cm
The thickness of silver = 0.5 cm, so the outer radius(R) = 2 + 0.5 = 2.5 cm
The volume of a hemisphere(V) = 2/3πr3 [r = radius]
Vsiler = Vouter - Vinner
⇒ Vsiler = 2/3πR3 - 2/3πr3
⇒ Vsiler = 2/3π(R3 - r3)
⇒ Vsiler = 2/3π((2.5)3 - (2)3)
⇒ Vsiler = 2/3π(15.625 - 8)
⇒ Vsiler = 2/3 × 3.14 × 7.625
⇒ Vsiler = 15.96 cm3