Question

the volume and height of a cylinder are 30.8 cm^3 and 5 cm respectively.Find the total surface area of the cylinder​

Answer 1

Answer:

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Answer 2

Given

• Volume = 30.8 cm³
• Height = 5 cm

Explanation:

Let the Radius of the Cylinder be x

Formula

$\maltese {\pmb{\boxed{\underline{\sf{ Volume_{(Cylinder)} = πr^2h }}}}}$

Then, Equation be like :-

$\colon\implies{\sf{ Volume_{(Cylinder)} = πr^2h }} \\ \\ \\ \colon\implies{\sf{ 30.8 = \dfrac{22}{7} \times (x)^2 \times 5 }} \\ \\ \\ \colon\implies{\sf{ \dfrac{30.8 \times 7}{22 \times 5} = x^2 }} \\ \\ \\ \colon\implies{\sf{ x^2 = 1.96 }} \\ \\ \\ \colon\implies{\large{\pmb{\sf{ x= \sqrt{1.96} = 1.4 \ cm }}}}$

Therefore, Radius of Cylinder is 1.4 cm.

Now, We can find the total Surface Area of the Cylinder as:

$\maltese {\large{\pmb{\boxed{\underline{\sf{ T.S.A. _{(Cylinder)} = 2πrh+2πr^2 }}}}}} \\ \\ \\ \colon\implies{\sf{ T.S.A. _{(Cylinder)} = 2πr(h+r) }} \\ \\ \\ \colon\implies{\sf{T.S.A. _{(Cylinder)} = 2 \times \dfrac{22}{ \cancel{7} } \times \cancel{1.4} (5+1.4) }} \\ \\ \\ \colon\implies{\sf{T.S.A. _{(Cylinder)} = 2 \times 22 \times 0.2 \times 6.4}} \\ \\ \\ \colon\implies{\sf{T.S.A. _{(Cylinder)} = 56.32 \ cm^2. }}$

Hence,

$\\ {\underline{\sf{The \ Total \ Surface \ Area \ of \ Cylinder \ is \ 56.32 \ cm^2. }}}$