# What will be the Thickness of Gold? If

A ball of lead 4 cm in diameter is covered with gold. If the volume of the gold and lead are equal, Then the thickness of gold

- 5.038 cm
- 5.190 cm
- 1.038 cm
- 0.519 cm

**Answer: (4) 0.519 cm**

**Explanation:-**

The volume of lead = the volume of gold

Diameter = 4 cm

Let be the total diameter is D & d = 4 cm

According to the question,

D = the thickness of the gold x 2 + d ………………………………. (1)

Then,

pie x d^{3}/6 = pie (D^{3}– d^{3})/6

d^{3} = D^{3} – d^{3
}d^{3}+ d^{3} = D^{3
}2d^{3} = D^{3
}D^{3} = 2 (4)^{3
}D^{3 } = 2 x 64

D^{3} = 128

D = 5.038 (cube root of both side)

Put the value of D in equation (1)

5.038 = 2 x thickness of the gold + 4

thickness of the gold = (5.038 – 4)/2

= 1.038/2

= .519 cm

Hence, the answer is (4) .519 cm