Step-by-step explanation:
Appropriate QuestioN :
- The volume of a cylinder is 108π cm³ and its height is 12 cm. What is the length of the cylinder's radius?
Need to FinD :
- We have to find the length of the cylinder's radius.
[tex] \red{\frak{Given}} \begin{cases} & \sf{Volume\ of\ the\ cylinder\ =\ {\pmb{\sf{108{\pi}\ cm^3.}}}} \\ & \sf{Height\ of\ the\ cylinder\ =\ {\pmb{\sf{12\ cm.}}}} \end{cases}[/tex]
We know that,
- The volume of a cylinder is the density of the cylinder which shows the amount of material contained in the cylinder.
- The volume of the cylinder is given by, πr²h.
Where,
- r is for radius.
- h is for height.
[tex]\rule{200}{3}[/tex]
- Now, let's calculate the length of the cylinder's radius.
[tex] \sf \dashrightarrow {Volume\ of\ cylinder\ =\ {\pi}r^2h} \\ \\ \\ \sf \dashrightarrow {108{\pi}\ =\ {\pi}r^2h} \\ \\ \\ \sf \dashrightarrow {108{\cancel \pi}\ =\ {\cancel \pi}r^2 \times 12} \\ \\ \\ \sf \dashrightarrow {108\ =\ r^2 \times 12} \\ \\ \\ \sf \dashrightarrow {\dfrac{\cancel{108}}{\cancel{12}}\ =\ r^2} \\ \\ \\ \sf \dashrightarrow {r^2\ =\ 9} \\ \\ \\ \sf \dashrightarrow {r\ =\ \sqrt{9}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{r\ =\ 3\ cm.}}}}_{\sf \blue{\tiny{Radius\ of\ cylinder}}}} [/tex]
∴ Hence, the length of the cylinder's radius is 3 cm.
