We need radius
Now
LSA
Answer:
813.4 cm² (nearest tenth)
Step-by-step explanation:
Volume of a cylinder
[tex]\sf V=\pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
Use the Volume of a Cylinder formula and the given values to find the radius of the cylinder:
[tex]\implies \sf 1715=\pi r^2 (18)[/tex]
[tex]\implies \sf r^2=\dfrac{1715}{18 \pi}[/tex]
[tex]\implies \sf r=\sqrt{\dfrac{1715}{18 \pi}[/tex]
Surface Area of a Cylinder
[tex]\sf SA=2 \pi r^2 + 2 \pi r h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Substitute the given value of h and the found value of r into the formula and solve for SA:
[tex]\implies \sf SA=2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)^2 + 2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)(18)[/tex]
[tex]\implies \sf SA=2 \pi \left(\dfrac{1715}{18 \pi} \right) + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)[/tex]
[tex]\implies \sf SA=\dfrac{1715}{9} + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)[/tex]
[tex]\implies \sf SA=813.3908956...[/tex]
Therefore, the surface area of the cylinder is 813.4 cm² (nearest tenth)
