Question

10. A right circular cylinder of height 7 cm has a curved surface area of 211.2 cm? find its volume.
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Answer 1

Answer:

✒ Volume of cylinder = 506.4cm³

Step-by-step explanation:

Given that,

• Height of cylinder (h) = 7cm
• Curved surface area of cylinder = 211.2 cm²

As we know that,

✒ Curved surface area of cylinder = 2πrh

➡ 211.2 = 2πrh

➡ 211.2 = 2 × 3.14 × r × 7

➡ 211.2 = 6.28 × 7r

➡ 211.2 = 43.96r

➡ r = 4.8cm

Now, we know that,

✒ Volume of cylinder = πr²h

➡ Volume of cylinder = 3.14 × (4.8)² × 7

➡ Volume of cylinder = 3.14 × 23.04 × 7

➡ Volume of cylinder = 506.4cm³.

Answer 2

Given:-

• Height of right circular cylinder is 7 cm.
• Curved surface area of right circular cylinder is 211.2 cm².

To find:-

• Volume of cylinder.

Solution:-

• First we will find Radius of cylinder by using Curved surface area of cylinder beacuse we do not have Radius of cylinder and Radius is needed in volume of cylinder.So,

We know that,

$\large \boxed{ \sf Curved \: surface \: area \: of \: cylinder = 2\pi rh}$

In which,

• r is Radius of cylinder.
• h is height of cylinder.

Height of cylinder = 7 cm.

Curved surface area of cylinder = 211.2 cm².

Put Height and Curved surface area in formula,

$\implies \sf 211.2 = 2 \times \dfrac{22}{7} \times r \times 7$

$\implies \sf 211.2 = 2 \times 22 \times r$

$\implies \sf 211.2 = 44r$

$\implies \sf \dfrac{211.2}{44} = r$

$\implies \sf 4.8 = r$

Or, r = 4.8

Radius of cylinder is 4.8 cm.

$\large \boxed{ \sf Volume \: of \: cylinder = \pi {r}^{2} h}$

In which,

• r is Radius of cylinder.
• h is height of cylinder.

r = Radius = 4.8 cm.

h = height = 7 cm.

Put r and h in formula,

$\implies \sf \dfrac{22}{7} \times {(4.8)}^{2} \times 7$

$\implies \sf 22 \times {(4.8)}^{2}$

$\implies \sf 22 \times 23.04$

$\implies \sf 506.88$

Therefore,

Volume of cylinder is 506.88 cm³.