Question

The curved surface area of a cylinder is 4400 CM square and the circumference of its base is 110 cm .Find the height and the volume of the cylinder

Answer 1

here is the answer
r = 17.5 cm
h = 40 cm
volume = 38500

Answer 2

The height of the cylinder is 40 cm.

The volume of the cylinder is 38500 cm³.

Step-by-step-explanation:

We have given that,

Curved surface area of cylinder = 4400 cm²

Circumference of base = 110 cm

We have to find the height and volume of the cylinder.

Now, we know that,

Circumference of circular base = 2 π r

⇒ 110 = 2 * ( 22 / 7 ) * r

⇒ r = ( 110 * 7 ) / ( 22 * 2 )

⇒ r = 110 ÷ 22 * 7 / 2

⇒ r = ( 5 * 7 ) / 2

⇒r = 35 ÷ 2

⇒ r = 17.5

Now, we know that,

Curved surface area of cylinder = 2 π r h

⇒ 4400 = ( 2 π r ) * h

⇒ 4400 = 110 * h

⇒ h = 4400 / 110

⇒ h = 440 / 11

⇒ h = 40 cm

∴ The height of the cylinder is 40 cm.

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Now, we know that,

Volume of cylinder = π r² h

⇒ Volume of cylinder = ( 22 / 7 ) * 17.5 * 17.5 * 40

⇒ Volume of cylinder = 22 * 17.5 ÷ 7 * 17.5 * 40

⇒ Volume of cylinder = 22 * 2.5 * 700

⇒ Volume of cylinder = 55 * 700

⇒ Volume of cylinder = 38500 cm³

∴ The volume of the cylinder is 38500 cm³.