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Measurement Integration Project Worksheet
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Measurement Integration Project Worksheet
A storage warehouse is made from a rectangular prism with a triangular-prism roof. The warehouse is 24 m long and 12 m wide. Its rectangular walls are 7 m high. The roof cross-section is an isosceles triangle with a 12 m base and a vertical height of 5 m. Use these measurements for every question. Exclude the ground from painting calculations. Give answers to a sensible degree of accuracy.
Calculations
Show your working and include units.
1.The roof cross-section forms a right-angled triangle with a vertical side of 5 m and a horizontal side of 6 m. Use Pythagoras’ theorem to calculate the sloping roof length.
2.Find the angle of elevation of the roof slope above the horizontal. Use the 5 m roof height and 6 m half-width.
3.Calculate the total exterior area to be painted: the four rectangular walls, both triangular gable ends, and both sloping roof faces. Do not include the ground.
4.Work out the warehouse’s total storage volume by adding the rectangular section and the triangular-prism roof section.
Costs and comparison
The painting contractor charges $14.50 per square metre. Monthly storage rent is $9.25 per cubic metre.
5.Using your painted area, estimate the total painting cost at $14.50 per square metre.
6.If every cubic metre is rented for a full month at $9.25, what is the warehouse’s monthly rental income?
7.Write the ratio of rectangular-section volume to roof-section volume in simplest form.
8.Divide the painting cost by the total storage volume to find the painting cost per cubic metre. Use your unrounded area and cost if possible.
9.Suppose the roof is made steeper while the warehouse length, width, and wall height stay fixed. Explain how this change affects the roof’s sloping length, painted area, and storage volume.
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