Question

Find the area of base and radius of a cylinder if its curved surface area is 990 sq cm and height is 15 cm.​

Answer 1

Answer:

the radius of a cylinder is 10.5 cm

the area of base is 346.5 cm

Step-by-step explanation:

given ,

height = 15cm

curved surface area = 990cm2

=> 2πrh = 990

=> 2 × 22/7 × r × 15 = 990

=> 2 × 22/7 × r = 990 / 15

=> 2 × 22/7 × r = 66

=> 2 × r = 66 × 7 / 22

=> r = 21 / 2

=> r = 10.5 cm

Now , area of base of cylinder = πr^2

= 22/7 × 10.5 × 10.5

= 346.5

Answer 2

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

• Curved surface area of the cylinder = 990cm

• Height of the cylinder = 15cm

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

• Radius of the cylinder

• Area of the base

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

$\odot$ Here we have given that the curved surface area of the cylinder is 990cm² and the height of the cylinder is 15cm, As we know that we have to find the area of the base and to find the area of the base we need radius of 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 area of base.

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

$\bigstar$ Let us find out the radius of the cylinder by assuming the radius be x cm, and after assuming the radius we will substitute the values in the formula ( Curved surface area = 2πrh )

• Let the radius be = x

$\qquad\sf{:\implies\:Curved\:Surface\:area\:of\:the\:cylinder\:=\:2\: \pi\:r\:h}$

$\qquad\sf{:\implies\:990\:=\:2\: \times\:\dfrac{22}{7}\:\times\:x\:\times\:15\:}$

$\qquad\sf{:\implies\:990\:=\:30\:\times\dfrac{22}{7}\:\times\:x\:}$

$\qquad\sf{:\implies\:\dfrac{990}{30}\:=\:\dfrac{22}{7\:}\:\times\:x}$

$\qquad\sf{:\implies\:33\:=\:\dfrac{22}{7\:}\:\times\:x}$

$\qquad\sf{:\implies\:\dfrac{33\:\times\:7}{22}\:=\:\:x}$

$\qquad\sf{:\implies\:\dfrac{3\:\times\:7}{2}\:=\:\:x}$

$\qquad\sf{:\implies\:\dfrac{21}{2}\:=\:\:x}$

$\qquad\sf{:\implies\:10.5\:=\:x}$

• Hence the radius of the cylinder is 10.5 cm.

$\bigstar$ Let us find out the area of the base by applying the formula ( Area of the base = πr² )

Radius = 10.5 cm

$\qquad\sf{:\implies\:Area\:of\:the\:base\:=\: \pi\:r^{2}}$

$\qquad\sf{:\implies\:Area\:of\:the\:base\:=\: \dfrac{22}{7}\:\times\:(10.5)^{2}}$

$\qquad\sf{:\implies\:Area\:of\:the\:base\:=\: \dfrac{22}{7}\:\times\:10.5\:\times\:10.5}$

$\qquad\sf{:\implies\:Area\:of\:the\:base\:=\: \dfrac{22}{7}\:\times\:110.25}$

$\qquad\sf{:\implies\:Area\:of\:the\:base\:=\: 346.36059\:cm^{2}}$

• Hence the area of the base is 346.36059 cm²