A fish tank is in the shape of an open glass cuboid 30cm deep with a base 16cm by 17cm,thesr measurements being external. If the glass is 0.5cm thick and it's density is 3g/cm3 find;
a) the capacity of the tank in litres
b) the mass of the tank in kg
a) The internal measurements of the fish tank can be found by subtracting twice the thickness of the glass from the external measurements:
Internal length = 16cm - 2(0.5cm) = 15cm
Internal width = 17cm - 2(0.5cm) = 16cm
Internal height = 30cm - 2(0.5cm) = 29cm
The capacity of the tank in liters is calculated by multiplying the internal length, width, and height together and then dividing by 1000 to convert to liters:
Capacity = (15cm x 16cm x 29cm) / 1000 = 7.68 liters
b) The volume of the glass can be found by subtracting the internal volume from the external volume:
External volume = 16cm x 17cm x 30cm = 8,160 cm^3
Internal volume = 15cm x 16cm x 29cm = 6,720 cm^3
Glass volume = External volume - Internal volume = 1,440 cm^3
The mass of the glass can be found by multiplying the glass volume by its density:
Mass = 1,440 cm^3 x 3 g/cm^3 = 4,320 g
Converting to kilograms:
Mass = 4,320 g / 1000 = 4.32 kg
Therefore, the mass of the tank is 4.32 kg.
To find the capacity of the tank in liters, we need to calculate the volume of the space inside the glass cuboid.
a) Volume of the glass cuboid:
The internal dimensions of the glass cuboid can be calculated by subtracting twice the thickness of the glass from the external dimensions.
Length = 16cm - 2(0.5cm) = 15cm
Width = 17cm - 2(0.5cm) = 16cm
Height = 30cm - 2(0.5cm) = 29cm
The volume of the glass cuboid can be calculated by multiplying its length, width, and height:
Volume = Length x Width x Height
Volume = 15cm x 16cm x 29cm
Volume = 6960 cm^3
To convert the volume from cubic centimeters to liters, we divide by 1000 (since there are 1000 cm^3 in a liter):
Capacity of the tank = 6960 cm^3 / 1000 = 6.96 liters
b) Mass of the tank:
The mass of the tank can be calculated by multiplying its volume by the density of the glass.
Mass = Volume x Density
Mass = 6960 cm^3 x 3 g/cm^3
Mass = 20880 g
To convert the mass from grams to kilograms, we divide by 1000 (since there are 1000 grams in a kilogram):
Mass of the tank = 20880 g / 1000 = 20.88 kg
Therefore,
a) the capacity of the tank is 6.96 liters.
b) the mass of the tank is 20.88 kg.