Question

find the curved surface area and the total surface area of a cylinder whose volume is
${30800}^{3}$
and radius of base is 14 cm​

Answer 1

Step-by-step explanation:

volume = πr*rh

30800= 22/7*14*14*h

30800= 616*h

h = 30800/616

h= 50

curved surface area of cylinder = 2πrh

= 2 * 22/7 * 14 * 50

=88*50

= 4400cm

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Answer 2

The CSA and TSA will be "4400 cm²" and "5632 cm²". Further explanation is given below.

Step-by-step explanation:

Given values:

The volume of a cylinder, V= 30800 cm³

Radius, r= 14 cm

As we know,

Volume= πr²h

On putting the values in the above formula, we get

⇒           V = $\frac{22}{7}$×(14)²×h

⇒ 30800  =  $\frac{22}{7}$×14×14×h

⇒ 30800  =  $\frac{22}{7}$×196×h

⇒  30800 = 616 × h

⇒             h=  $\frac{30800}{616}$

⇒            h = 50 cm

Now, Curved surface area, CSA = 2πrh

On putting the values in the above formula, we get

⇒ CSA = 2×$\frac{22}{7}$×14×50

⇒         = 2×22×2×50

⇒         = 44×100

⇒         = 4400 cm²

Total surface are, TSA = 2πr(r+h)

On putting the values in the above formula, we get

⇒  TSA = 2×$\frac{22}{7}$×14(14+50)

⇒          = 2×22×2(64)

⇒          = 88(64)

⇒          = 5632 cm²

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