Question

volume of cylinder is 6160cm cube find the radius of cylinder if height is 10 cm also find the total surface area of the cylinder​

Answer 1

Answer:

radius = 14cm

TSA = 2112 cm²

Step-by-step explanation:

Given , the volume of the cylinder, V = 6160 cm³

also, the height of the cylinder, h    = 10cm

we know , Volume of the cylinder  = $\pi$r²h cu.units

ie., $\pi$r²h = 6160 cm³

=> $\pi$r²(10) = 6160 cm³

=> $\pi$r² = 6160/10 cm²

=> $\pi$r² = 616 cm²

=> r² = 616*(7/22)cm²

=> r² = 28*7 cm²

=> r² = 196 cm²

=> r = √196 cm

=> r = 14 cm

we know, TSA of cylinder = 2$\pi$r(h+r) sq.units

                                           = 2*(22/7)*14*(10+14) cm²

                                           = 2*(22)*2*(24) cm²

                                           = 88*24 cm²

                                           = 2112 cm²

Answer 2

Question:-

Volume of cylinder is 6160cm cube. Find the radius of cylinder if height is 10cm. Also find the total surface area of the cylinder.

Required Answer:-

Given:-

$\\ \sf{\rightarrow{Volume\:of\:the\:cylinder = 6160 {cm}^{3} }}$

$\sf{\rightarrow{Height\:of\:the\:cylinder = 10cm}}$

To Find:-

$\\\sf{\rightarrow{Radius\:of\:the\:cylinder}}$

$\sf{\rightarrow{Total\:surface\:area\:of\:the\:cylinder}}$

Solution:-

As we know that:-

$\\ \underline{\boxed{\rm{\blue{\bold{Radius\:of\:a\:cylinder }= \sqrt{ \frac{V}{\pi h}}}}}}$

Where,

• V is for volume of the cylinder.
• h is for height of the cylinder.

Substituting the values:-

$\\ \sf{\bold{Radius\:of\:the\:cylinder = \sqrt{ \frac{6160}{ \frac{22}{7} \times 10} }}}$

$\\\sf{\implies{\bold{Radius\:of\:the\:cylinder} = \sqrt{ \frac{6160}{31.4285} } }}$

$\\\sf{\implies{\bold{Radius\:of\:the\:cylinder} = \sqrt{ 196.0044 } }}$

$\\\sf{\therefore{\bold{Radius\:of\:the\:cylinder} = 14.000015 / \red{14}}}$

$\\ \underline{\boxed{\rm{\green{Hence,\:radius\:of\:the\:cylinder = \bold{14cm}}}}}$

Again,

$\\\underline{\boxed{\blue{\bold{Total\:surface\:area\:of\:a\:cylinder} = 2\pi rh + 2\pi {r}^{2} }}}$

Substituting the values:-

$\\\sf{\bold{T.S.A. \:of\:the\:cylinder} = 2 \times \frac{22}{7} \times 14 \times 10 + 2 \times \frac{22}{7} \times {(14)}^{2} }$

$\\\sf{\bold{\implies{T.S.A. \:of\:the\:cylinder}} = 880 + 1232 }$

$\\\sf{\bold{\therefore{T.S.A. \:of\:the\:cylinder}} }=\red{2112}$

$\\ \underline{\boxed{\rm{\green{Hence,\:Total\:surface\:area\:of\:the\:cylinder = \bold{2112 {cm}^{2} }}}}}$