Answer:
The shell is best modeled by a cone.
[tex]SA=32\pi=100.6\text{ square inches}[/tex]
By the given choices, since the surface area is not a perfect cone, it has a small alteration at the bottom which increases the area. The approximate surface area of the shell is 107.4 square inches.
Step-by-step explanation:
The seashell is best represented by a cone. The surface area of a cone is represented by the following equation:
[tex]\begin{gathered} SA=\pi rs+\pi\cdot r^2 \\ \text{where,} \\ \\ r=\text{radius} \\ s=\text{ slant height} \end{gathered}[/tex]
Then, use the Pythagorean theorem to find the slant height:
[tex]\begin{gathered} s=\sqrt[]{2.5^2+10^2} \\ s=\frac{5\sqrt[]{17}}{2} \end{gathered}[/tex]
Now, solve for the surface area. If s=10.3, r=2.5
[tex]\begin{gathered} SA=\pi\cdot2.5\cdot\frac{5\sqrt[]{17}}{2}+\pi\cdot(2.5)^2 \\ SA=25.75\pi+6.25\pi \\ SA=32\pi=100.6\text{ square inches} \end{gathered}[/tex]
By the given choices, since the surface area is not a perfect cone, it has a small alteration at the bottom which increases the area. The approximate surface area of the shell is 107.4 square inches.
