Question

the diametre of cylinder is 14 cm and height 20cm. find the curved surface area and total surface area of the cylinder​

Answer 1

Answer :

• Curved surface area of cylinder is 880cm²
• Total surface area of cylinder is 1188cm²

Given :

• Diameter of cylinder is 14cm
• Height of cylinder is 20cm

To find :

• Curved surface area of cylinder
• Total surface area of cylinder

Solution :

First we need to find the radius by using the formula of radius

We know that

• Radius = Diameter/2

Where, Diameter is 14cm

➟ Radius = Diameter/ 2

➟ Radius = 14/2

➟ Radius = 7cm

Radius is 7cm

Finding the curved surface area of cylinder :

• Radius of cylinder is 7cm
• Height of cylinder is 20cm

We know that

• Curved surface area of cylinder = 2πrh

➟ Curved surface area of cylinder = 2πrh

➟ 2 × 22/7 × 7 × 20

➟ 2 × 22 × 20

➟ 880 cm²

Curved surface area of cylinder is 880cm²

Finding the Total surface area of cylinder :

• Radius of cylinder is 7cm
• Height of cylinder is 20cm

We know that

• Total surface area of cylinder = 2πr(h + r)

➟ Total surface area of cylinder = 2πr (h + r)

➟ 2 × 22/7 × 7 (20 + 7)

➟ 2 × 22 (27)

➟ 2 × 594

➟ 1188cm²

Total surface area of cylinder is 1188cm²

Hence,

• Curved surface area of cylinder is 880cm²
• Total surface area of cylinder is 1188cm²

Answer 2

$\underline{\underline{\sf{\maltese\:Given\::-}}}$

• Diameter of the cylinder = 14cm

• Height of the cylinder = 20cm

$\underline{\underline{\sf{\maltese\:To\:find\::-}}}$

• Curved surface area of the cylinder.

• Total surface area of the cylinder.

$\underline{\underline{\sf{\maltese\:Concept\::-}}}$

$\odot$ Here we have given that the Diameter of the cylinder is 14cm and the height of the cylinder is 20cm. As we known that to find the curved surface area or the total surface area of the cylinder we need radius of the cylinder so firstly we will find out the radius of the cylinder.

$\odot$ After finding the radius of the cylinder we will find out the curved surface area of the cylinder by substituting the given values in the formula ( Curved surface area = 2πrh ).

$\odot$ Now at last we will find out the total surface area of the cylinder by applying the formula ( Total surface area = 2πr( r + h ).

$\underline{\underline{\sf{\maltese\:Full\:solution\::-}}}$

$\bigstar$ Let us find out the radius of the cylinder by dividing the diameter by 2      ( Radius = diameter/2 ).

$\qquad\sf{:\implies\:Radius\:=\:\dfrac{Diameter}{2}}$

$\qquad\sf{:\implies\:Radius\:=\:\dfrac{14}{2}}$

$\qquad\sf{:\implies\:Radius\:=\:7\:cm}$

• Hence the radius of the cylinder is 7cm

$\bigstar$ Let us find out the curved surface area of the cylinder by substituting the given values in the formula ( Curved surface area = 2πrh ).

$\qquad\sf{:\implies\:Curved\:Surface\:Area\:of\:the\:cylinder\:=2\pi rh}$

$\qquad\sf{:\implies\:Curved\:Surface\:Area\:of\:the\:cylinder\:=2\:\times\:\dfrac{22}{7}\:\times\:7\:\times\:20}$

$\qquad\sf{:\implies\:Curved\:Surface\:Area\:of\:the\:cylinder\:=2\:\times\:22\times\:20}$

$\qquad\sf{:\implies\:Curved\:Surface\:Area\:of\:the\:cylinder\:=\:44\:\times\:20}$

$\qquad\sf{:\implies\:Curved\:Surface\:Area\:of\:the\:cylinder\:=\:880\:cm^{2}}$

• Hence the curved surface area of the cylinder is 880cm²

$\bigstar$ Let us find out the total surface area of the cylinder by substituting the given values in the formula ( Total surface area = 2πr ( r + h ).

$\qquad\sf{:\implies\:Total\:Surface\:Area\:of\:the\:cylinder\:=2\pi r\:(\:r\:+\:h\:)}$

$\qquad\sf{:\implies\:Total\:Surface\:Area\:of\:the\:cylinder\:=2\:\times\:\dfrac{22}{7}\:\times\:7\:(\:7\:+\:20\:)}$

$\qquad\sf{:\implies\:Total\:Surface\:Area\:of\:the\:cylinder\:=2\:\times\:\dfrac{22}{7}\:\times\:7\:(\:27\:)}$

$\qquad\sf{:\implies\:Total\:Surface\:Area\:of\:the\:cylinder\:=2\:\times\:22\:\times\:27\:}$

$\qquad\sf{:\implies\:Total\:Surface\:Area\:of\:the\:cylinder\:=44\:\times\:27\:}$

$\qquad\sf{:\implies\:Total\:Surface\:Area\:of\:the\:cylinder\:=\:1188\:cm^{2}}$

• Hence the total surface area of the cylinder is 1188 cm²

$\underline{\underline{\sf{\maltese\:Formula\:used\::-}}}$

• Radius = Diameter/2

• Curved surface area of the cylinder = 2πrh

• Total surface area of the cylinder = 2πr ( r + h)

$\underline{\underline{\sf{\maltese\:Request\::-}}}$

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