Question

the total surface area of a cylinder of diameter 14cm is 484cm2 find its height​

Answer 1

Given:-

• The Total Surface Area(TSA) of a cylinder of diameter 14cm is 484cm^2.

To Find:-

• Find the height of the cylinder.

Concept:-

• Let's go through the concept first. Concept used here is TSA of a Cylinder.Substitute the given values in the equation and solve it to find the height of the given cylinder.

Formulae Applied:-

• TSA of a Cylinder = 2πr (r + h)

Solution:-

TSA of the given cylinder = 484cm^2

Diameter = 14cm

Radius = 14/2 = 7cm

Height = ??

According to the question we have!

TSA of a cylinder = 2πr (r + h)

⟹ 2πr (r + h) = 484cm^2

⟹ 2 × 22/7 × 7(7 + h) = 484

⟹ 44(7 + h) = 484

⟹ 308 + 44h = 484

⟹ 44h = 484 - 308

⟹ 44h = 176

⟹ h = 176/44

⟹ h = 4

⟹ h = 4cm

Hence,

The height of the cylinder is 4cm.

Verification:-

2πr (r + h) = 484cm^2

h = 4

⟹ 2 × 22/7 × 7(7 + 4) = 484

⟹ 44 (11) = 484

⟹ 44 × 11 = 484

⟹ 484 = 484

⟹ LHS = RHS

Hence,

It is verified.

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