A glass (glass density ρ1 = 2.5 g / cm3) contains a volume V2 = 200 cm3 of water (water density ρ2 = 1000 kg / m3). What is the volume of the glass walls if its total mass is m = 0.35 kg?

A glass (glass density ρ1 = 2.5 g / cm³) contains a volume V2 = 200 cm³ of water (water density ρ2 = 1000 kg / m³). What is the volume of the glass walls if its total mass is m = 0.35 kg?

We know

ρ1 = 2.5 g / cm³
ρ2 = 1000 kg / m³
V2 = 200 cm³
m = 0.35 kg
V1 =?



Solution

according to the formula:

ρ = m / V


we have:

m1 = p1V1

m2 = p2V2

m = m1 + m2

m = p1V1  + p2V2

V1  = (m - p2V2) / p1

V1  = [0.35 kg - (1000 kg / m³ x 200 cm³)] / 2.5 g / cm³

V1 = [0.35 kg - (1000 kg / m³ x 0.0002 m³)] / 0.0025 kg / cm³

V1  = (0.35 kg - 0.2 kg) / 0.0025 kg / cm³

V1  = 0.15 kg / 0.0025 kg / cm³

V1 = 60 cm³


Legend
m = total mass (kg)
m1 = mass of water
m1 = mass of glass
glass density ρ1 = 2.5 g / cm³
water density ρ2 = 1000 kg / m³
V2 = volume of water
V1 = volume of the glass walls


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