The aquarium has a bottom area S = 32dm3 and height h = 60cm3. Determine the amount of water poured if the aquarium is half full.
The aquarium has a bottom area S = 32 dm ^ 2 = 3200 cm ^ 2 and a height h₀ = 60 cm.To determine the mass of poured water m through its volume V and density ρ, we use the formula: m = ρ ∙ V, where the volume of a body the shape of a rectangular parallelepiped is found by the formula: V = S ∙ h. We get:
m = ρ ∙ S ∙ h.
From the condition of the problem it is known that the density of water is ρ = 1 g / cm ^ 3 and the aquarium is half filled with water, that is, the height of the water is h = h₀ / 2, which means:
m = ρ ∙ S ∙ h₀ / 2.
Substitute the values of the quantities into the calculation formula:
m = (1 g / cm ^ 3 ∙ 3200 cm ^ 2 ∙ 60 cm) / 2; m = 96000 g = 96 kg.
Answer: the mass of water in the aquarium is 96 kg.
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