Question

A right cylinder has a circumference of 16 π cm . Its height is half the radius. Identify the lateral area and the surface area of the cylinder.

Answer 1

The lateral area is 32π  sqcm and the surface area of the cylinder is 4096π² sqcm.

What is a right cylinder?

A right cylinder is a cylinder whose sides are perpendicular to its base.

It is given that-.

circumference of cylinder = 16 π cm

Suppose, r is radius of the cylinder,

h is height of the cylinder.

Then,

⇒ 2 π r = 16 π

⇒ r = 8 cm.

It is also given that,

height = 1/2radius

⇒ h = 1/2r

⇒ h = 1/2 * 8 cm

⇒ h = 4 cm

Now,∵ lateral area of cylinder =  2 π r h

∴ lateral area of cylinder =  16*  π * 4

⇒ lateral area of cylinder = 32π  sqcm.

Similarly, surface area of the cylinder  =  2 π r h * 2 π r²

⇒ surface area of the cylinder  =  2 π r h * 2 π (8)²

⇒ surface area of the cylinder  =  32π * 2 π 64

⇒ surface area of the cylinder  =  4096 * π² sqcm

Hence,the lateral area is 32π  sqcm and the surface area of the cylinder is 4096π² sqcm.

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