Question

a home gardener is building a greenhouse in the shape of a hemisphere. the radius of the hemisphere is 13.3 meters, and construction costs are $25 per 100 square meters. what is the total cost of construction? $106.72 $1,111.43 $553.46 $277.86

Explanation:

Step1: Calculate the surface area of the hemisphere

The surface area formula for a hemisphere is \(A = 2\pi r^{2}\). Given \(r = 13.3\) meters.

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Step2: Calculate the cost per square - meter

The cost is \(\$25\) per \(100\) square - meters. So the cost per square - meter \(c=\frac{25}{100}=\$0.25\) per square - meter.

Step3: Calculate the total cost

The total cost \(T = A\times c\). Substitute \(A = 1110.87\) and \(c = 0.25\)

$$T=1110.87\times0.25=\$277.72\approx\$277.80$$

Answer:

\(\$277.80\)