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 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

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 _____________
A. 2 cm	B. 10 cm	C. 0.5 cm	D. 1 cm
Right Option : D
View 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 ______________
A. $2 pi h^2$	B. $frac {3}{2} pi h^2$	C. $frac {4}{3} pi h^2$	D. $pi h^2$
Right Option : B
View Explanation

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