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

If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is ______________

Right Option : B
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Explanation
 
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