# 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

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