Question

the lateral surface area of a cylinder is 1056cm² and it's height is 10cm find radius of cylinder ​

Answer 1

$\Large{\underbrace{\sf{\purple{Required\:Answer:}}}}$

Given :

• The lαterαl surfαce αreα of α cylinder is 1056cm².
• The height of the cylinder is 10cm.

To find :

• Rαdius of the cylinder.

Knowledge Required :

• $\large{\boxed{\sf{\purple{ L.S.A_{(cylinder)} = 2\pi rh}}}}$

Where, π = 22/7 or 3.14

r = rαdius

h = height

Solution :

• Substitute the vαlues in the formulαe of L.S.A(lαterαl surfαce αreα) of the cylinder.

$\longrightarrow{\sf{ 1056cm^{2} = 2 \times \dfrac{22}{7} \times (r) \times 10cm}}$

$\longrightarrow{\sf{ 1056cm^{2} = (r)\times \dfrac{2\times 22\times 10}{7}}}$

$\longrightarrow{\sf{ 1056cm^{2} = (r) \times \dfrac{440}{7}}}$

• Trαnspose 440/7 to R.H.S.

$\longrightarrow{\sf{\dfrac{ 1056cm^{2} \times 7}{440cm} = (r)}}$

• Multiply 1056 with 7.

$\longrightarrow{\sf{ (r)=\dfrac{7,392cm^{2}}{440cm}}}$

• Divide 7,392cm² with 440cm.

$\large\implies{\boxed{\sf{\purple{ (r) = 16.8cm}}}}$

Hence, the rαdius of the cylinder is 16.8cm.

And we αre done ! :)

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