A small sculpture made of brass (rho brass = 8470 kg/m 3) is believed to have a secret central cavity. The weight of the sculpture in air is 15.76 N. When it is submerged in water, the weight is 13.86 N. What is the volume of the secret cavity?

Volume of secret cavity = 4 x 10⁻⁶m³

Explanation:

The weight of the sculpture in air is 15.76 N

Mass of the sculpture = 1.61 kg

Mass = Volume x Density

1.61 = V x 8470

Volume of brass = 1.90 x 10⁻⁴ m³

When it is submerged in water, the weight is 13.86 N.

That is

Weight of sculpture - Weight of water displaced = 13.86 N

15.76 - Weight of water displaced = 13.86

Weight of water displaced = 1.9 N

Mass of water displaced = 0.194 kg

Mass = Volume x Density

0.194 = V x 1000

Volume of water displaced = 1.94 x 10⁻⁴ m³

Volume of secret cavity = Volume of water displaced - Volume of brass material

Volume of secret cavity = 1.94 x 10⁻⁴-1.94 x 10⁻⁴ = 0.04x 10⁻⁴ = 4 x 10⁻⁶m³