Final answer:
The total surface area of the top and bottom surfaces of the harpsichord case is 35,478 sq cm. The area of each side of the harpsichord case is 23,508 sq cm. The value of the timber used to construct the case is €2,189.16.
Step-by-step explanation:
To find the surface area of the top and bottom surfaces of the harpsichord case, we need to calculate the area of each surface and then add them together. The formula for the area of a rectangle is length multiplied by width.
Surface area of top and bottom = 2(length x width) = 2(219 cm x 81 cm) = 35,478 sq cm. Therefore, the total surface area of the top and bottom surfaces of the harpsichord case is 35,478 sq cm.
To find the area of each side of the harpsichord case, we need to calculate the area of each rectangular side. The formula is length multiplied by height.
Area of each side = length x height = 2(219 cm x 31 cm) + 2(81 cm x 31 cm) + 2(219 cm x 81 cm) = 23,508 sq cm. Therefore, the area of each side of the harpsichord case is 23,508 sq cm.
To calculate the value of the timber used to construct the case, we need to find the total surface area of the case and multiply it by the cost per square meter of timber.
Total surface area = (2 x top and bottom surface area) + (4 x side surface area) = 2(35,478 sq cm) + 4(23,508 sq cm) = 170,968 sq cm.
Converting the total surface area to square meters: 170,968 sq cm ÷ 10,000 = 17.0968 sq m.
Value of the timber = total surface area x cost per square meter = 17.0968 sq m x €128 = €2,189.16.