Question

a harpsichord case has the dimensions shown.
a find the area of the top and bottom surfaces.
b find the area of each side of the case.
c if the timber costs $128 per square metre, find the cost of the timber to construct this case.

Explanation:

Step1: Calculate area of top and bottom surfaces

The top and bottom surfaces are rectangles with length \(l = 219\) cm and width \(w=81\) cm. The area of a rectangle is \(A = l\times w\). For two surfaces, \(A_{top - bottom}=2\times(219\times81)\).

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Step2: Calculate area of each side

There are two pairs of sides.

• Front - back sides: Rectangles with length \(l = 219\) cm and width \(w = 34\) cm. Area of two surfaces \(A_{front - back}=2\times(219\times34)\)

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• Left - right sides: Rectangles with length \(l = 81\) cm and width \(w = 34\) cm. Area of two surfaces \(A_{left - right}=2\times(81\times34)\)

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Step3: Calculate total surface area and cost

Total surface area \(A_{total}=35478 + 14892+5508=55878\space cm^{2}\). Convert to \(m^{2}\): \(A_{total}=\frac{55878}{10000}=5.5878\space m^{2}\). Cost \(C=128\times5.5878\)

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Answer:

a. The area of the top and bottom surfaces is \(35478\space cm^{2}\)
b. The area of front - back sides is \(14892\space cm^{2}\) and the area of left - right sides is \(5508\space cm^{2}\)
c. The cost of the timber is approximately \(\$715.24\)