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​

2 thoughts on “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​”

1. 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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   • [tex]\sf{\blue{Curved\:Surface\:Area\:=\:2 \pi rh}}[/tex]

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   [tex]\:\:\:\:\:\:\:\:\dashrightarrow\:{\sf{2 \pi rh\:=\:88cm}^{2}}[/tex]

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   [tex]\:\:\dashrightarrow\:\sf{2\:\times\:{\dfrac{22}{7}}\:\times\:r\:\times\:14cm\:=\:88}[/tex]

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   [tex]\:\:\:\:\:\:\:\:\dashrightarrow\:{\sf{r\:=\:{\dfrac{88\:\times\:7}{2\:\times\:22\:\times\:14}}}}[/tex]

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   [tex]\:\:\:\:\:\:\:\:\:\:\:\:\dashrightarrow{\sf{r\:=\:1cm}}[/tex]

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

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   • [tex]\sf{\blue{Diameter\:=\:2\:\times\:radius}}[/tex]

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   [tex]\:\:\:\:\:\:\:\:\dashrightarrow\:{\sf{2\:\times\:1}}[/tex]

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   [tex]\:\:\:\:\:\:\:\:\dashrightarrow\:{\sf{2}}[/tex]

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

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2. 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

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