Question

A flower bed is in the form of a rectangle with semi-circular ends. The rectangle is 25m long and the flower bed is 14m wide. The cost of black soil is ¢89.50 per square meter, and the cost of labor is ¢800.00 per square meter. Find the cost of covering the flower bed with black soil. If the cost is in Ghanaian Cedis (¢), what is the correct expression for the total cost?

a. 0.5 * pi * 25 * 14 * 89.50 + 25 * 14 * 800.00
b. 0.5 * pi * 25 * 14 * 89.50
c. pi * 25 * 14 * 89.50 + 25 * 14 * 800.00
d. pi * 25 * 14 * 89.50

Answer 1

To find the cost of covering the flower bed with black soil, calculate the total area of the flower bed and multiply it by the cost per square meter of black soil. Add the cost of labor to find the total cost.

Step-by-step explanation:

To find the cost of covering the flower bed with black soil, we need to find the total area of the flower bed and then multiply it by the cost per square meter of black soil.

The flower bed is in the form of a rectangle with semi-circular ends, so we can split it into three parts: the rectangle in the middle and the two semi-circles on the ends.

The area of the rectangle is 25m * 14m = 350m².

The area of each semi-circle is 0.5 * π * (14/2)²

= 153.94m².

Therefore, the total area is 350m² + 2 * 153.94m²

= 657.88m².

To find the cost, we multiply the total area by the cost per square meter of black soil: 657.88m² * ¢89.50/m² = ¢58792.02.

Adding the cost of labor, the expression for the total cost is 657.88m² * ¢89.50/m² + 25m * 14m * ¢800.00/m²

= ¢58792.02 + ¢280000

= ¢338792.02.