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

A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find its total curved surface area.

Right Option : A
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Explanation
Question : 2

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
Question : 3

The students of a school were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with the base, using cardboard. Each pen holder was to be of radius 3 cm and height 10.5 cm. The school was to supply the competitors with cardboard. If there were 35 competitors, how much card board was required to be bought for the competition? (in sq cm)

Right Option : C
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Explanation
 
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