Question

8. The lateral surface area of a cylinder of length 14 m is 220 m². Find the volume
the cylinder
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Answer 1

Answer:

$\huge\underline{\overline{\mid{\bold{\orange{ANSWER-}}\mid}}}$

Given height h = 14m.

Given lateral surface area = 220

              2 * pi * r * h = 220

              2 * 22/7 * r * 14 = 220

              2 * 22 * r * 14 = 1540

              616 r = 1540

                    r = 1540/61

                      = 2.5 m.

Volume of cylinder = pi * r * r * h

                                 = 22/7 * (2.5) * (2.5) * 14

                                 = 275.

Hope this helps!

$\huge\underline\mathcal \pink{Divi}$

Answer 2

Given:-

• Lateral Surface Area of cylinder = 220 m²
• Length of cylinder = 14 m

To Find:-

Volume of the cylinder.

Solution:-

We know,

Lateral Surface Area of cylinder = 2πrh

Hence,

$\sf{220 = 2\times\dfrac{22}{7}\times r \times 14}$

= $\sf{220 = 2\times \dfrac{22}{\cancel{7}}\times r \times \cancel{14}}$

= $\sf{220 = 2\times 22 \times r \times 2}$

= $\sf{220 = 88r}$

= $\sf{\dfrac{220}{88} = r}$

= $\sf{r = 2.5\:m}$

Now,

Radius (r) = 2.5 m

Length (h) = 14 m

Volume of cylinder = πr²h cu.units

$\sf{Volume = \dfrac{22}{7}\times (2.5)^2 \times 14}$

= $\sf{Volume = \dfrac{22}{\cancel{7}}\times 2.5\times 2.5\times \cancel{14}}$

= $\sf{Volume = 22\times 2.5\times 2.5\times 2}$

= $\sf{Volume = 275\:m^3}$

Hence the volume of cylinder is 275 m³.

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$\bf{\underline{\large{Additional\:Information!!!}}}$

• Volume of cylinder = πr²h cu.units

• Lateral Surface Area (LSA) of cylinder = 2πrh sq.units

• Total Surface Area (TSA) of cylinder = 2πr(r+h) sq.units.

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Note!

Lateral Surface Area (LSA) is also known as Curved Surface Area (CSA).

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