Question

$the \: volume \: of \: the \: cylinder \: is448\pi ^{2} \: and \: its \: height \: is \: 7cm \: find \: its \: radius$
​

Answer 1

Given :

• Volume of Cylinder is 448πcm²
• Height of Cylinder is 7cm.

To Find :

• Radius of Cylinder.

Solution :

$\longmapsto\tt{Height=7cm}$

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cylinder=\pi{{r}^{2}h}}$

Putting Values :

$\longmapsto\tt{448{\cancel{\pi}}={\cancel{\pi}}\times{{r}^{2}}\times{7}}$

$\longmapsto\tt{\cancel\dfrac{448}{7}={r}^{2}}$

$\longmapsto\tt{\sqrt{64}=r}$

$\longmapsto\tt\bold{r=8cm}$

So , The Radius of the cylinder is 8cm...

_______________________

• C.S.A of Cylinder = 2πrh
• T.S.A of Cylinder = 2πr(r+h)
• Volume lf Cylinder = πr²h

_______________________

Answer 2

Question:-

The volume of the cylinder is 448π cm² and its height is 7cm. Find its radius ?

Formula used:-

Volume of a cylinder = πr²h

Answer:-

Given: Volume = πr²h = 448π

$\sf{\pi r^2 h = 448 \pi^2 \\ \implies \pi \:r^2\: 7 = 448 \pi}$

$\implies\sf{\cancel{\pi}\: r^2 7 = 448\cancel{\pi}}$

$\sf{\implies r^2 = \dfrac{448}{7} \\ \implies r^2 = 64 \\ \implies r = \sqrt{64} \\ \implies r = 8 cm}$

$\red{\boxed{\bf{Radius\:=\:8cm}}}$

$\rule{400}{4}$

$\begin{array}{|c|c|}</p><p>\cline{1-2}</p><p>\multicolumn{2}{|c|}{\textsf{Other important formulae}} \\</p><p>\cline{1-2} \textsf{C.S.A. of a cylinder} & \sf{2\pi r h} \\</p><p>\cline{1-2} \textsf{T.S.A. of cylinder} & \sf{2 \pi r (r + h)} \\</p><p>\cline{1-2}</p><p>\end{array}$