Question

4. The curved surface area of a cylinder is
8800 cm2. If the radius of a cylinder is 28 cm,
find its volume.​ ​

Answer 1

Clarification :

Here, as per the given question, we have C.S.A of the cylinder that is $\sf { 8800\: {cm}^{2} }$ and the radius of the cylinder that is 28 cm. Now, we have to find out its volume.

We'll calculate the volume by the given formula :

• $\rm { {Volume}_{Cylinder} =( \pi {r}^{2} h) \: cubic \: units }$

But, as we don't have the value of its height, so firstly we'll calculate the height by taking it as a variable and making a suitable equation with the help of C.S.A of cylinder.

Then, we'll substitute all the values in the formula of volume of the cylinder in order to get the answer.

Given:

• C.S.A of cylinder = $\sf { 8800 \: {cm}^{2} }$

• Radius (r) = 28 cm

To calculate:

• Volume of the cylinder.

Calculation:

We know that,

$\star \: \: {\underline {\boxed {\large {\sf \pink { {Volume}_{(Cylinder)} = \pi {r}^{2}h } }}}}$

~Let us calculate the height first.

$\bigstar \: \underline{\boldsymbol{According \: to \: the \: Question:}} \\ \\ \\ \sf{ \longrightarrow {C.S.A}_{(Cylinder)} =2 \pi rh } \\ \\ \\ \sf{ \longrightarrow 8800 =2 \times \dfrac{22}{7} \times 28 \times h} \\ \\ \\ \sf{ \longrightarrow 8800 \: {cm}^{2} = 176 \: cm \times h \: cm } \\ \\ \\ \sf{ \longrightarrow \dfrac{8800 \: cm^2}{176 \: cm}=h \: cm } \\ \\ \\ \longrightarrow \underline{\boxed{\sf{Height = 50 \: cm}}} \: \red{\bigstar}$

~Now, calculating volume of the cylinder:

$\star \: \: {\underline {\boxed {\large {\sf \pink { {Volume}_{(Cylinder)} = \pi {r}^{2}h } }}}} \\ \\ \\ \sf{ \longrightarrow \: {Volume}_{(Cylinder)} = \dfrac{22}{7} \times {(28)}^{2} \times 50 \: {cm}^{3} } \\ \\ \\ \sf{ \longrightarrow \: {Volume}_{(Cylinder)} = \dfrac{22}{7} \times 28 \times 28 \times 50 \: {cm}^{3} } \\ \\ \\ \sf{ \longrightarrow \: {Volume}_{(Cylinder)} = 22 \times 4\times 28 \times 50 \: {cm}^{3} } \\ \\ \\ \longrightarrow \: \underline{\boxed{\sf{{Volume}_{(Cylinder)} =123200 \: {cm}^{3} }}} \: \red{\bigstar}$

Henceforth, volume of the cylinder is 123200 cubic centimetre.

More formulae:

• C.S.A of cylinder = 2πrh
• T.S.A of cylinder = 2πr(r+h)
• Volume of cylinder = πr²
• C.S.A of cube = 4s²
• T.S.A of cube = 6s²
• Volume of cube = s × s × s
• Volume of cuboid = l × b × h
• T.S.A of cuboid = 2(lb + lh + bh)
• C.S.A of cuboid = 2(l+b) × h

» T.S.A and C.S.A are always calculated in square units.

» Volume is always calculated in cubic units.

Answer 2

We know, if radius is (r) and height (h), then

CSA = 2πrh

Radius given = 28 cm

CSA = 8800 cm^2

∴ 2πrh = 8800

⇒ 22/7 × 28h = 4400

⇒ 22 × 4h = 4400

⇒ h = (4400)/(22 × 4)

⇒ h = 50 cm

Now, volume = πr²h

So, V = 22/7 × 28 × 28 × 50 cm^3

⇒ V = 123200 cm^3

∴ The volume of the object was of 123200 cm^3.