a) To find the internal dimensions of the tank, we subtract twice the thickness of the glass from the external dimensions:
Length = 16cm - 2(0.5cm) = 15 cm
Width = 17cm - 2(0.5cm) = 16 cm
Height = 30cm - 2(0.5cm) = 29 cm
The capacity of the tank is given by the formula: Volume = Length x Width x Height
Volume = 15cm x 16cm x 29cm = 6960 cm^3
To convert the volume to litres, we divide by 1000 (since 1 litre = 1000 cm^3):
Volume = 6960 cm^3 / 1000 = 6.96 litres
Therefore, the capacity of the tank is 6.96 litres.
b) To find the mass of the tank, we need to calculate the volume of the glass used in the tank:
Volume of glass = (15cm x 16cm x 29cm) - (16cm x 17cm x 30cm) = 6960 cm^3 - 8160 cm^3 = 1200 cm^3
The mass of the glass is given as 3g/cm^3, so the total mass of the glass used in the tank is:
Mass = 1200 cm^3 x 3g/cm^3 = 3600g
To convert the mass to kilograms, we divide by 1000:
Mass = 3600g / 1000 = 3.6 kg
Therefore, the mass of the tank is 3.6 kg.
A fish tank is in the shape of an open glass cuboid 30 cm deep with a base 16cm by 17cm, these measurements being external.if the glass is 0.5cm thick and its mass is 3g/ cm^3, find
( a) the capacity of the tank in litres,and
( b) the mass of the tank in kg.
1 answer