Question

the
28. A rectangular sheet of cardboard having dimensions
20 cm by 16 cm is rolled into a cylinder of height
16 cm. Find the volume of the cylinder thus formed.​

Answer 1

Given -

A rectangular sheet of cardboard having dimensions 20 cm by 16 cm is rolled into a cylinder of height 16 cm.

To find -

• Volume of the cylinder

Solution -

• Length of rectangle = circumference of the cylinder

→ 2πr = 20 cm

→ πr = 20/2

→ 22/7 × r = 10

→ r = 10 × 7/22

→ r = 35/11 cm

• Width of rectangle = height of the cylinder = 16cm

According to the question

→ Volume of cylinder

→ πr²h

→ 22/7 × 35/11 × 35/11 × 16

→ 2 × 5 × 35/11 × 16

→ 350 × 16/11

→ 5600/11

→ 509.09 cm³

•°• Volume of the cylinder = 509.09 cm³

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Answer 2

Answer:

Given :-

• A rectangular sheet of cardboard having dimensions of 20 cm by 16 cm is rolled into a cylinder of height 16 cm.

To Find :-

• What is the volume of the cylinder formed.

Formula Used :-

★ Circumference of cylinder = 2πr ★

✪ Volume of cylinder = πr²h ✪

Solution :-

❶ First we have to find the radius of a cylinder,

Given :

• Length = 20 cm

According to the question by using the formula we get,

⇒ 2πr = 20

We know that, π = 22/7

⇒ 2 × 22/7 × r = 20

⇒ 22/7 × r = 20/2

⇒ 22/7 × r = 10

⇒ r = 10 × 7/22

⇒ r = 70/22

➠ r = 35/11 cm

Hence, the radius of a cylinder is 35/11 cm .

❷ Now we have to find the volume of a cylinder,

Given :

• Width or height = 16 cm
• Radius = 35/11 cm

According to the question by using the formula we get,

↦ Volume of cylinder = πr²h

↦ Volume of cylinder = 22/7 × (35/11)² × 16

↦ Volume of cylinder = 22/7 × 35/11 × 35/11 × 16

↦ Volume of cylinder = 10 × 35/11 × 16

↦ Volume of cylinder = 160 × 35/11

➦ Volume of cylinder = 509.09 cm³

∴ The volume of cylinder is 509.09 cm³ .