Question

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The curved surface area of a cylinder is 4400cm2 and the circumference of its base is 220cm2. find the volume of the cylinder
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Answer 1

Answer:

$\huge\bf\underline\pink{Answer}$

Given :-

➻ Curved surface area of the Cylinder

⠀⠀⠀⠀⠀⠀⠀⠀= 4400cm²

➻ Circumference of the base of cylinder

⠀⠀⠀⠀⠀⠀⠀⠀⠀= 220cm

To Find :-

⠀⠀⠀⠀➻ Radius of the Cylinder

⠀⠀⠀⠀➻ Height of the Cylinder

⠀⠀⠀⠀➻ Volume of the Cylinder

Solution :-

Circumference of the base = 2πr

Since,

It is given that circumference of base = 220cm

∴ 2πr = 220cm

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

$\implies\sf{r = \cancel{220}^{10}\times\dfrac{7}{\cancel{22} } \times\dfrac{1}{2} }$

$\implies\sf{r = \dfrac{\cancel{10}^{5} \times 7}{\cancel{2} }}$

$\implies\sf\purple{r = 35cm}$

According to the question,

Curved surface area of cylinder = 4400cm²

• Formula of curved surface area of cylinder = 2πrh

So, 2πrh = 4400cm

$\implies\sf{2 \times\dfrac{22}{\cancel{7}}\times \cancel{35 }^{5} \times h = 4400 {cm}^{2}}$

$\implies\sf{220\times h = 4400{cm}^{2}}$

$\implies\sf{h = \dfrac{4400}{220}cm}$

$\implies\sf\purple{h = 20cm}$

∴ Height of the Cylinder is 20cm

Volume of the Cylinder = πr²h

$\implies\sf{\dfrac{22}{7}\times(35) ^{2} \times 20 }$

$\implies\sf{ \dfrac{22}{\cancel{7} } \times \cancel{1225}^{175} \times 20}$

$\implies\sf{(22 \times 175 \times 20) {cm}^{3} }$

$\implies\bold\purple{77000 {cm}^{3} }$

Hence,

The Volume of the Cylinder is 77000cm³ ✔︎

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Answer 2

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