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

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)
A. 7928	B. 7933	C. 7920	D. 7925
Right Option : C
View Explanation

Question : 2

Find the surface area of a can with radius of 7.7 cm and height 12.3 cm.
A. 953 sq cm	B. 968 sq cm	C. 768 sq cm	D. 568 sq cm
Right Option : B
View Explanation

Question : 3

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.
A. Radius=8, Height=8/2	B. Radius=7, Height=7/2	C. Radius=8, Height=8/6	D. Radius=4, Height=8/2
Right Option : B
View Explanation

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