Question

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

Answer 1

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

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

Answer 2

Correct Question :

• The curved surface area of a cylinder is 4400cm² and the circumference of its base is 220cm².

• Find the volume of the cylinder

Given :

• Curved surface area of a cylinder = 4400cm²

• Circumference of base = 220cm²

To find :

• Volume of the cylinder.

Formulae used :

• Circumference of base = 2πr

• Curved surface area of a cylinder = 2πrh

• Volume of the cylinder = πrh

Explanation :

We know that circumference of the base = 2πr

The given Circumference of the base = 220cm²

We can write it as 2πr = 220cm²

• 2 × $\bf\dfrac{22}{7}$ × r = 220cm²

• r = $\bf{\cancel{220}^{10}}$ × $\sf\dfrac{\cancel{22}}{7}$ × $\bf\dfrac{1}{2}$

• r = $\sf\dfrac{\cancel{10}^{5}{× 7}}{\cancel{2}}$

• r = 35cm.

We know that curved surface area of a cylinder = 2πrh

It is given that curved surface area of a cylinder = 4400cm²

We can write it as 2πrh = 4400cm²

• 2 × $\sf\dfrac{22}{\cancel{7}}$ × $\bf{\cancel{(35)}^{5}}$ × h = 4400cm²

• 220 × h = 4400cm²

• h = $\sf\dfrac{\cancel{4400}}{\cancel{220}}$

• h = 20cm

➥ Hꫀίցнt ꪮғ tнꫀ ᥴყᥣίꪀძꫀɾ = 20cm

We know that volume of the cylinder = πrh

By substituting the values,

• $\bf\dfrac{22}{7}$ × $\bf{(35)}^{2}$ × 20

• $\sf\dfrac{22}{\cancel{7}}$ × $\bf{\cancel{1225}^{175}}$ × 20

• (22 × 175 × 20) cm³

• 77000cm³

Answer :

⟿ Therefore the volume of the cylinder is 77000cm³