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.
A. 953 sq cm	B. 968 sq cm	C. 768 sq cm	D. 568 sq cm
Right Option : B
View 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.
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 : 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 _____________
A. 2 cm	B. 10 cm	C. 0.5 cm	D. 1 cm
Right Option : D
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Problems On Boats And Stream

Rules For Divisibility

Square and Square Root

Profit Loss and Discount

Simple and Compound Interest

Ratio and Proportion

Partnership and Mixture

Time, Speed and Distance

Quadratic Equations

Time and Work

Mensuration

Surface Area and Volume

Permutation and Combination

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Andhra Bank

Class / Course

IBPS PO Prelims

IBPS Clerk Prelims

IBPS PO Prelims Test Series

SBI SO General Aptitude

Bank PO Prelims

Bank Clerical Prelims

Bank AO Prelims

Bank SO Prelims

Quantitative Aptitude Proficiency

Verbal Ability Proficiency

Bank Of Baroda AO Prelims

LIC ADO Prelims

LIC AAO Prelims

IBPS Clerk Prelims Test Series

IBPS RRB Prelims Test Series

IBPS SO Prelims Test Series

SBI PO Prelims Test Series

SBI Clerical Prelims Test Series

SBI SO General Aptitude Test Series

Bank PO Prelims Test Series

Bank Clerical Prelims Test Series

Bank AO Prelims Test Series

Bank SO Prelims Test Series

Quantitative Aptitude Test Series

EXIM AO Prelims Test Series

Verbal Ability Test Series

Bank Of Baroda AO Prelims Test Series

LIC ADO Prelims Test Series

LIC AAO Prelims Test Series

Students / Parents Reviews [10]

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre f...

Archit Segal

7th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from m...

Prisha Gupta

8th

About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has...

Shreya Shrivastava

8th

My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.

Hiya Gupta

8th

One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develo...

Aman Kumar Shrivastava

10th

It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice

Barkha Arora

10th

My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak poi...

Shivam Rana

7th

View All

Attention !!!!!