Question

The lateral surface area of a cylinder of length 14m is 220 m^2 find the volume of cylinder.

Answer 1

height = 14 m

lateral surface are=2πrh
$220 = 2 \times \frac{22}{7} \times r \times 14$
220=88r
$radius = \frac{220}{88}$
therefore,
radius = 2.5 cm

$volume = \pi {r}^{2} h$
$= \frac{22}{7} \times {(2.5)}^{2} \times 14$
$volume = 275 {m}^{3}$
is the answer.

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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