We are given –
- Height of cylinder is = 4cm
- Lateral surface area of cylinder is = 24πcm²
We are asked to find volume of the given cylinder.
Let the radius be "r".Then according to the question,it’s given –
[tex]\qquad[/tex] [tex]\pink{\twoheadrightarrow\bf Curved\: surface\: area _{(Cylinder)}= 2\pi r h }[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 2\pi r h = 24 \pi[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 2\cancel{\pi} rh = 24 \cancel{\pi}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r =\dfrac{24}{2h}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \dfrac{24}{2\times 4}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \dfrac{24}{8}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \cancel{\dfrac{24}{8}}[/tex]
[tex]\qquad[/tex] [tex]\pink{\twoheadrightarrow\bf r = 3 \: cm}[/tex]
Now, Let's find volume of cylinder
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf V_{(Cylinder)} = \pi {r}^{2}h}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 3^2\times 4 [/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 9 \times 4[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 36[/tex]
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf V_{(Cylinder)} = 36 \pi \: cm^3}[/tex]
- Henceforth, volume of cylinder is 36π cm³.
