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Sagot :
Solution
Step 1
Find the lateral surface area
The lateral surface area of any shape is the area of other parts of the object excluding the base area
Therefore the expression for the surface area of a hemisphere is given as
[tex]A\text{ = 2}\times\pi\times r^2[/tex]From the image of the image in the question,
radius(r) = diameter/2 = 5/2 yard
pi = 3.14
Substituting all these into the above formular give us the lateral surface area as
[tex]\begin{gathered} A\text{ = 2}\times3.14\times(\frac{5}{2})^2 \\ A=39.25yard^2 \\ \end{gathered}[/tex]Hence the lateral area is 39.25 square yard
From the options, the closest to this is 39.27 square yards
Step 2
Calculate the total surface area
The total surface area of a hemisphere is expressed as
[tex]3\times\pi\times r^2[/tex]After substitution, the total surface area is given as
[tex]\begin{gathered} 3\times3.14\times(\frac{5}{2})^2 \\ =58.875yard^2 \\ \approx\text{ The total surface area is given as} \\ 58.9yard^2 \end{gathered}[/tex]Hence the total surface area = 58.9 square yard
Step 3
Find the volume
The expression for the volume of a hemisphere is given as
[tex]V\text{ = 2/3}\times\pi\times r^3[/tex]Substituting in the values the volume is given as
[tex]\begin{gathered} V\text{ = }\frac{2}{3}\times3.14\times(\frac{5}{2})^3 \\ V=32.71yard^3 \end{gathered}[/tex]From the question the closest answer to the volume based on approximation is 32.72 cubic yard
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