Question

The volume of a cylindrical can is 3.08 litre. If the area of its base is 154 cm², find its curved surface area​

Answer 1

879.8 cm² (nearest tenth)

Explanation:

Given:

• Volume = 3.08 L
• Area of base = 154 cm²

Convert the given volume to cubic centimeters:

`\boxed{\begin{aligned}1\; \sf L&=1000\; \sf cm^3\\\\\implies 3.08\; \sf L&=3.08 * 1000\\&=3080\; \sf cm^3\end{aligned}}`

Substitute the volume and base area into the formula for the volume of a cylinder and solve for height, h:

`\boxed{\begin{aligned}\textsf{Volume of a cylinder}&= \sf area\;of\;base * height\\\\\implies 3080&=154h\\h&=(3080)/(154)\\h&=20\;\; \sf cm\end{aligned}}`

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:

`\boxed{\begin{aligned}\textsf{Area of a circle}&= \pi r^2\\\\\implies 154&=\pi r^2\\r^2&=(154)/(\pi)\\r&=\sqrt{(154)/(\pi)}\;\; \sf cm\end{aligned}}`

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:

`\boxed{\begin{aligned}\textsf{LSA of a cylinder}&=2\pi r h\\\\\implies \sf LSA&=2 \pi \left(\sqrt{(154)/(\pi)}\right) (20)\\& = 879.8229537...\\&=879.8\;\; \sf cm^2\end{aligned}}`