Total Surface Area of Cylinder


 
 
Concept Explanation
 

Total Surface Area of Cylinder

A Cylinder of radius r and height h. The total surface area or TSA includes area of circular top and base as well as the curved surface area or CSA.

Length of rectangle= Circumference of base = large 2pi r                                                                                                                                                                          

Breadth of rectangle = h

TSA = Area of base + Area of top + CSA of cylinder

     large =pi r^2 + pi r^2 + 2pi r h

    =2pi r^2 + 2pi r h

    =2pi r(r +h)

Illustration: A solid cylinder has total surface area of 462 cm^2.  Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.

Solution: Given:   Curved surface area  =frac {1}{3} times Total;Surface;Area

Rightarrow     2 pi rh = frac {1}{3} times (2 pi rh + 2 pi r^2)

2 pi rh = frac {1}{3} times(2pi r) (r+h)

h = frac {1}{3} times (r+h)

3h =r+h

3h -h=r

2h=r

r=2h  ...................(i)

Now, given that total surface area = 462

Rightarrow  Curved surface area  =frac {1}{3} times 462

Rightarrow  2pi rh=154

Using equation (i0, we have

2pi (2h)h=154

4pi h^{2}=154

h^{2}=frac{154}{4pi }

h^{2}=frac{154}{4}times frac{7}{22}

h^{2}=frac{7}{4}times 7

h^{2}=frac{49}{4}

h=sqrt{frac{49}{4}}

h=pm frac{7}{2}

As hneq - frac{7}{2}

So, h = frac{7}{2}

Hence height of cylinder = 3.5 cm

Using equation (i), we have

and radius of cylinder = r = 2h

                                     = 2times frac{7}{2}

                                     = 7 cm

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Find the surface area of a can with radius of 7.7 cm and height 12.3 cm.

Right Option : B
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Explanation
Question : 2

A solid cylindrical tank has total surface area of 462 sq cm. Its curved surface area is one third of its total surface area. Find the radius and the height of the cylinder.

Right Option : B
View Explanation
Explanation
Question : 3

If the curved surface area and the radius of a base of a cylinder are 8.8 cm sq and 0.7 cm respectively, then the height of cylinder is _____________

Right Option : D
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Explanation
 
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