Question

Curved surface area of a cylinder is 44 cm square and circumference of the base is 8.8cm, find the volume of the cylinder.​

Answer 1

Given :

• Curved surface area of a cylinder is 44 cm².
• Circumference of the base is 8.8cm.

To find :

• The volume of the cylinder =?

Formula Used :

• Circumference of circle = 2πr.
• Curved Surface area of cylinder = 2πrh
• The volume of a cylinder = πr²h

Step-by-step explanation :

As We know that,

Circumference of circle = 2πr.

And, in the above question it is given that circumference of the base is 8.8cm. So,

2πr = 8.8 cm

πr = 8.8/2

πr = 4.4

r = 4.4 ÷ 22/7

r = 4.4 × 7/22

r = 1.4

Therefore, We got the Radius (r) = 1.4 cm.

Now, As We know that,

Curved Surface area of cylinder = 2πrh

Substituting the values in the above formula, we get,

44 = 8.8 × h [ ∵ 2πr = 8.8]

h = 44/8.8

h = 5

Therefore, We got the value of height (h) = 5 cm.

Now,

The volume of a cylinder = πr²h

Substituting the values in the above formula, we get,

= 22/7 × π × (1.4)² × 5

= 22/7 × π × 1.4 × 1.4 × 5

= 22 × π × 0.2 × 1.4 × 5

= 30.8π

Therefore, The volume of a cylinder = 30.8π cm³.

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Curved surface area of cylinder = 44cm²
• Circumference of the base =8.8cm

${\bf{\blue{\underline{To\:Find:}}}}$

• Volume of the cylinder =?

${\bf{\blue{\underline{Now:}}}}$

$\longrightarrow{\sf{ cimcumference = 2\pi \: r}}$

$\longrightarrow{\sf{ 8.8 = 2\pi \: r}}$

$: \implies{\sf{ curved \: surface \: area \: of \: cylinder = 44}}$

$: \implies{\sf{ 2\pi rh = 44}}$

$: \implies{\sf{ 2\pi rh = 44}}$

$: \implies{\sf{ 8.8h = 44}}$

$: \implies{\sf{ h = \frac{44}{8.8} }}$

$: \implies\boxed{\sf{ h = 5}}$

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Also

$\longmapsto{\sf{ 2\pi \: r = 110}}$

$\longmapsto{\sf{ 2 \times \frac{22}{7} \times \: r = 8.8}}$

$\longmapsto{\sf{ \frac{44}{7} \times \: r = 8.8}}$

$\longmapsto{\sf{ \: r = 8.8 \times \frac{7}{44} }}$

$\longmapsto{\sf{ \: r = 1.4 }}$

__________________________________

$\longrightarrow \boxed{\sf{volume \: of \: cylinder \: = \pi \: {r}^{2}h }}$

$: \implies{\sf{ \pi \times ( {1.4)}^{2} \times 5 }}$

$: \implies{\sf{ \pi \times 1.96 \times 5 }}$

$: \implies{\sf{ \pi \times 9.8 }}$

$: \implies{\sf{ \frac{22}{7} \times 9.8 }}$

$: \implies{\sf{ 30.799c {m}^{3} }}$