A block of concrete is 1m long, 50cm wide and 4cm thick. Calculate the volume of the block in cm^3. If 1cm^3 has a mass of 2.7g, find the mass of the block in kg.
Volume of the block = length x width x thickness
= 100cm x 50cm x 4cm
= 20,000 cm^3
Mass of the block = volume x density
Density of concrete is typically around 2,400 kg/m^3 or 2.4 g/cm^3.
Therefore, the mass of the block would be:
20,000 cm^3 x 2.4 g/cm^3 = 48,000 g
1 kg = 1000 g, so the mass of the block in kg would be:
48,000 g ÷ 1000 = 48 kg
Answer: The volume of the block is 20,000 cm^3 and the mass of the block is 48 kg.
Student said the density is 2.7 g/cm^3
If the student dismissed the typical density of concrete and used a density value of 2.7 g/cm^3, then the mass of the block should be recalculated:
Volume of the block = length x width x thickness
= 100cm x 50cm x 4cm
= 20,000 cm^3
Mass of the block = volume x density
= 20,000 cm^3 x 2.7 g/cm^3
= 54,000 g
To get the mass of the block in kg:
54,000 g ÷ 1000 = 54 kg
Therefore, if the density of the concrete used by the student is 2.7 g/cm^3, then the mass of the concrete block is 54 kg.
To calculate the volume of the block in cm^3, we'll use the formula:
Volume = Length x Width x Height
Given:
Length = 1 m = 100 cm
Width = 50 cm
Height = 4 cm
Plugging in these values:
Volume = 100 cm x 50 cm x 4 cm
= 200,000 cm^3
Therefore, the volume of the block is 200,000 cm^3.
To find the mass of the block in kg, we'll use the conversion factor given:
1 cm^3 = 2.7 g
Given:
Volume = 200,000 cm^3
To convert the volume to grams, we'll multiply it by the conversion factor:
Mass in grams = Volume x Conversion factor
= 200,000 cm^3 x 2.7 g/cm^3
= 540,000 g
To convert the mass from grams to kilograms, we'll divide by 1000:
Mass in kg = Mass in grams / 1000
= 540,000 g / 1000
= 540 kg
Therefore, the mass of the block is 540 kg.