1.

A ball of lead 4 cm in diameter, is covered with gold. If the volume of gold and the lead are equal, what is the approximate thickness of gold? (Given 3√2 = 1.259)1). 5.038 cm2). 5.190 cm3). 1.038 cm4). 0.518 cm

Answer»

⇒ Volume of LEAD = (4/3) π × 23

⇒ Volume of GOLD = Total volume – Volume of lead

⇒ (4/3) π × (2 + x)3 – (4/3) π × 23

According to question,

⇒ (4/3) π × 23 = (4/3) π × (2 + x)3 – (4/3) π × 23

⇒ (2 + x)3 = 2 × 23

⇒ 2 + x = 2 × 3√2

⇒ x = (2 × 3√2) – 2

⇒ 2(3√2 – 1)

⇒ 2(1.259 – 1)

⇒ 2 × 0.259 = 0.518 cm


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