# Volume of a Cylinder

# Surface Area of a Cylinder

Home | Online Math Tutoring | 6th Grade Math Tutoring | **Volume and Surface Area of Cylinder**

## How do you calculate the volume of a cylinder?

When we roll up a piece of square or rectangular piece of paper, we get a cylinder.

* (Note: Diameter is twice the radius)*

We measure the area of a circle by using the formula –

When we find the volume of a cylinder, it is 3-dimensional shape, so just the height is multiplied additionally with the area of a circle which is the formula for volume of cylinder.

### Volume of a Cylinder

*Example:* The radius of a cylindrical bottle is 3 cm and length is 7 cm. What is the maximum volume of juice the jar can contain? (Take = )

Volume =

= × 3 × 3 ×7

=198 cm³

## How do you find the surface area of the cylinder?

The area of the rectangular sheet of paper is equal to the curved surface area of the cylinder.

The length of the sheet is equal to the circumference of the circular base which is equal to 2r.

So, **curved surface area of the cylinder** = Area of the rectangular sheet = length × width = perimeter of the base of the cylinder × *h* = **2***rh*

*Example:* Find the surface area of a tube of length 8 cm, diameter 14 cm.

Diameter = 14 cm

So, radius = diameter/2= = 7cm

Curved Surface Area = 2 × ×7 ×8

= 352 cm²

## How do you find the total surface area of a cylinder?

As discussed earlier, a cylinder is something which looks like a rolled up rectangle.

Now to calculate the TSA, we are left with two circles on the top and the bottom.

Area of the circle on top and the base circle when the cylinder is closed on both ends.

*Example: *Find the total surface area of a cylinder with closed top and bottom which has a radius of 7 cm and height 5 cm.

Hence the total surface area is = {2 × × 7 × 5} + {2 × × 7 × 7}

= 220 + 308

Total Surface Area of the cylinder = **528 cm ^{2}**

### Check Point

- What is the volume of cylinder witch height 8 cm and total surface area 1936 cm
^{2}? (Take = ) - Mark has a kiosk for lemonade at his school fair and has a cylindrical vessel which is of height 21 cm and radius of 4 cm. What volume of lemonade does he need to make to fill his vessel? (Take = )
- A cylinder is of height 49 cm is having radius of 5 cm. Find the curved surface area of the cylinder. (Take = )

4. How much volume of coffee does a cylindrical thermos of diameter 10 cm and height 14 cm hold? (Take = )

- Find the height of a cylindrical vessel of curved surface area 1320 mm² and radius 14 mm. (Take = )
- What is the height of a pipe with closed valves on both ends which has a total surface area of 8800 cm² and radius of 14 cm? (Take = )

##### Answer key

- 4928 cm³
- 1056 cm³
- 1540 cm²
- 1100 cm²
- 15 mm
- 86 cm

+1-269-763-4602

+1-269-763-5024

#### Quick Links

#### Follow Us

#### Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.

Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.

Our ‘*Learning by Design*’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘*What do you want to learn today?*’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.

The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.

All tutoring sessions are recorded and made available for a month so you can review concepts taught.

Email or call our support team with any issues or questions – we are here for you 24X7.

Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!

Thousands have taken the eTutorWorld Advantage – what are you waiting for?

© 2019 eTutorWorld - Online Tutoring and Test Prep | All rights reserved