The exerxise aids as correctly identified are both hemispheres.
At the base, each of these hemispheres has a measure around it as 25 inches. This measure represnts the circumference of the circular surface at the base. We can use this bit of information to determine the radius as follows;
[tex]\text{Circumference}=2\pi r[/tex]
Where the circumference is given as 25, and the value of pi is taken as 3.14, we would now have;
[tex]25=2\times3.14\times r[/tex]
We cross multiply this and we arrive at;
[tex]\begin{gathered} \frac{25}{2\times3.14}=r \\ \frac{25}{6.28}=r \\ r=3.98089\ldots \end{gathered}[/tex]
Rounded to two decimal places, we now have the radius as;
[tex]r\approx3.98[/tex]
The formula for the surface area of a hemisphere is given as;
[tex]\text{Area}=3\pi r^2[/tex]
We now substitute for the value of the radius and we have the following;
[tex]\begin{gathered} \text{Area}=3\pi r^2 \\ \text{Area}=3\times3.14\times3.98^2 \\ \text{Area}=9.42\times15.8404 \\ \text{Area}=149.2166in^2 \end{gathered}[/tex]
Note however that the total surface area is an addition of the following;
[tex]\text{Total surface area}=Curved\text{ surface area}+Base\text{ area}[/tex]
The base area is
[tex]\begin{gathered} \text{Base area}=\pi r^2 \\ \text{Base area}=3.14\times3.98^2 \\ \text{Base area}=3.14\times15.8404 \\ \text{Base area}=49.7388in^2 \end{gathered}[/tex]
Therefore we now have the surface area as follows;
[tex]\begin{gathered} \text{Total area}-Base\text{ area}=surface\text{ area} \\ 149.2166-49.7388=\text{surface area} \\ 99.4778=surface\text{ area} \end{gathered}[/tex]
Rounded to two decimal places, this now becomes;
ANSWER:
[tex]\text{Area}=99.47in^2[/tex]
