A gold bar has a trapezium cross sectional area. Gold has a de city of 19.3 grams per cm^3 . Work out the mass of the gold bar. Give your answer in kilograms
To work out the mass of the gold bar, we need to calculate the volume of the bar first.
The formula for the volume of a trapezium-shaped prism is given by:
Volume = Area of the trapezium cross-section x Length
Since the cross-sectional area is given as a trapezium, we need to find the area using the formula for the area of a trapezium:
Area = (a + b) * h / 2
Where 'a' and 'b' are the lengths of the parallel sides of the trapezium and 'h' is the perpendicular height.
Once we have the volume, we can then calculate the mass using the density of gold, which is given as 19.3 grams per cm^3.
Since the mass is expected to be in kilograms, we will convert the final answer from grams to kilograms by dividing by 1000.
Let's assume the dimensions of the trapezium cross-section are as follows:
Parallel sides: a = 8 cm, b = 13 cm
Perpendicular height: h = 5 cm
Length of the gold bar: L = 20 cm
Now let's substitute the values into the formulas to find the mass.
First, calculate the area of the trapezium:
Area = (a + b) * h / 2
Area = (8 + 13) * 5 / 2
Area = 21 * 5 / 2
Area = 105 / 2
Area = 52.5 cm^2
Next, calculate the volume of the gold bar:
Volume = Area of the trapezium cross-section * Length
Volume = 52.5 cm^2 * 20 cm
Volume = 1050 cm^3
Finally, calculate the mass of the gold bar using the density of gold:
Mass = Volume * Density
Mass = 1050 cm^3 * 19.3 grams per cm^3
Mass = 20265 grams
To convert grams to kilograms, divide by 1000:
Mass = 20265 grams / 1000
Mass = 20.265 kilograms
Therefore, the mass of the gold bar is approximately 20.265 kilograms.