Answer:
879.8 cm² (nearest tenth)
Step-by-step explanation:
Given:
- Volume = 3.08 L
- Area of base = 154 cm²
Convert the given volume to cubic centimeters:
[tex]\boxed{\begin{aligned}1\; \sf L&=1000\; \sf cm^3\\\\\implies 3.08\; \sf L&=3.08 \times 1000\\&=3080\; \sf cm^3\end{aligned}}[/tex]
Substitute the volume and base area into the formula for the volume of a cylinder and solve for height, h:
[tex]\boxed{\begin{aligned}\textsf{Volume of a cylinder}&= \sf area\;of\;base \times height\\\\\implies 3080&=154h\\h&=\dfrac{3080}{154}\\h&=20\;\; \sf cm\end{aligned}}[/tex]
The base of a cylinder is a circle.
Substitute the given area of the base into the formula for the area of a circle and solve for radius, r:
[tex]\boxed{\begin{aligned}\textsf{Area of a circle}&= \pi r^2\\\\\implies 154&=\pi r^2\\r^2&=\dfrac{154}{\pi}\\r&=\sqrt{\dfrac{154}{\pi}}\;\; \sf cm\end{aligned}}[/tex]
The curved surface area of a cylinder is called the Lateral Surface Area (LSA).
Substitute the found radius and height into the formula for LSA of a cylinder:
[tex]\boxed{\begin{aligned}\textsf{LSA of a cylinder}&=2\pi r h\\\\\implies \sf LSA&=2 \pi \left(\sqrt{\dfrac{154}{\pi}}\right) (20)\\& = 879.8229537...\\&=879.8\;\; \sf cm^2\end{aligned}}[/tex]
