Answer:
To calculate the length of the gold bar, we need to first calculate the area of the trapezium cross-section, using the formula for the area of a trapezium:
Area = (a + b) x h / 2
where a and b are the lengths of the parallel sides of the trapezium, and h is the height.
From the diagram, we can see that a = 4 cm, b = 10 cm, and h = 7 cm. Substituting these values into the formula, we get:
Area = (4 + 10) x 7 / 2 = 49 cm^2
We can now calculate the length of the gold bar by dividing its volume by its cross-sectional area:
Length = Volume / Area = 165 / 49 = 3.3673 cm (to 4 decimal places)
Therefore, the length of the gold bar is approximately 3.3673 cm.
For the second part of the question, we can use the formula for the volume of a prism to calculate the height of the similar bar of gold:
Volume = Area x Height
where Area is the area of the trapezium cross-section, and Height is the height of the gold bar.
From the given information, we know that Volume = 675.84 cm^3, and we have already calculated Area to be 49 cm^2. Substituting these values into the formula, we get:
675.84 = 49 x Height
Height = 675.84 / 49 = 13.793 cm (to 3 decimal places)
Therefore, the height of the similar bar of gold is approximately 13.793 cm.
For the third part of the question, we need to rearrange the formula V = h^2 y to make h the subject. We can start by dividing both sides by y:
V / y = h^2
Next, we can take the square root of both sides:
sqrt(V / y) = h
Therefore, the formula rearranges to:
h = sqrt(V / y)
This gives us the height of the bar of gold in terms of its volume and the value of y.
Explanation:
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