Question

the curved surface area of a right circular cylinder of height 14 cm is 88 cm2. find the diameter of the base of the cylinder​

Answer 1

Answer :

• Diameter of the base of the cylinder is 2cm

Given :

• The curved surface area of a right circular cylinder of height 14cm is 88cm²

To find :

• The diameter of the base of the cylinder

Solution :

• Let the diameter of the base of the cylinder be r

• Height is 14cm
• Curved surface area of a right circular cylinder is 88cm²

As we know that,

• Curved surface area of cylinder = 2πrh

》Curved surface area of cylinder = 2πrh

》88 = 2πrh

》88 = 2 × 22/7 × r × 14

》r = 88 × 7 / 2 × 22 × 14

》r = 1cm

Radius is 1cm

Now , we have to find the Diameter of the base of the cylinder:

We know that,

• Diameter = 2 × r

》Diameter = 2 × r

》2 × 1

》2cm

Hence,Diameter of the base of the cylinder is 2cm

Answer 2

Given :

• Height of Cylinder = 14cm
• Curved Surface Area of Cylinder = 88cm²

Find : Diameter of the Base of the Cylinder.

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★ Now, first we find Curved Surface Area :

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• $\sf{\blue{Curved\:Surface\:Area\:=\:2 \pi rh}}$

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$\:\:\:\:\:\:\:\:\dashrightarrow\:{\sf{2 \pi rh\:=\:88cm}^{2}}$

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$\:\:\dashrightarrow\:\sf{2\:\times\:{\dfrac{22}{7}}\:\times\:r\:\times\:14cm\:=\:88}$

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$\:\:\:\:\:\:\:\:\dashrightarrow\:{\sf{r\:=\:{\dfrac{88\:\times\:7}{2\:\times\:22\:\times\:14}}}}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\dashrightarrow{\sf{r\:=\:1cm}}$

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$\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━$

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★ Now, we find the Diameter of the base of the cylinder.

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• $\sf{\blue{Diameter\:=\:2\:\times\:radius}}$

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$\:\:\:\:\:\:\:\:\dashrightarrow\:{\sf{2\:\times\:1}}$

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$\:\:\:\:\:\:\:\:\dashrightarrow\:{\sf{2}}$

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$\:\therefore\:{\underline{\sf{Hence, \:the\:Diameter\: of\:the\: base\: of \:the \:cylinder\:is\:{\textsf{\textbf{ 2\:cm}}}}}}.$

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