Table of Contents

## Definition of Total Surface Area of Right Circular Cylinder

The **Total Surface Area of Right Circular Cylinder** may be defined as the surface area of the total cylinder including the two bases (top and the bottom). Therefore, the **Total Surface Area** is the sum of the **Curved Surface area** and the area of the two circular faces which are at the top and the bottom.

## Total Surface Area of Right Circular Cylinder Formula

The figure below represents the Total Surface Area of Right Circular Cylinder.

Therefore, the **Total Surface Area of Right Circular Cylinder** will be,

Total Surface Area = Curved Surface Area + Area of Top Face + Area of Bottom Face

Let the radius of the cylinder is r

Therefore,

Area of the top face =\pi r^2

Area of the bottom face = \pi r^2

Therefore, the Total Surface Area will be,

Total Surface Area = 2\pi r h+\pi r^2+\pi r^2

Total Surface Area =2\pi r h+2\pi r^2

Total Surface Area =2\pi r(r+h)

## Solved Examples

### 1. The Curved Surface Area of a Right Circular Cylinder of height 21 cm is 100 sq.cm. Find the diameter of the base of the cylinder?

**Solution:**

Given,

Height of the Cylinder, h=21\,cm

Curved Surface Area of the Cylinder, CSA=100 cm^2

We know that,

Curved Surface Area\,=2\pi rh

Therefore,

100 cm^2=2\pi rh

100 cm^2=2 \times \frac{22}{7} \times r\times 21

r=\frac{25}{33}

r=0.75 cm

The diameter of the cylinder is, D = 2\times r= 2\times 0.75 =1.5\,cm

### 2. It is required to make a closed cylindrical tank of height 2 meters and base diameter of 280 cm from a metal sheet. How many square meters of sheet is required for the same?

**Solution:**

Given,

Height of the cylinder, h = 2 m

Diameter of the cylinder, D = 280 cm = 0.28 m

Therefore, the Radius of the Cylinder, r= 0.14 m

Since the cylindrical tank is closed, the amount of sheet is required is equal to the total surface area of the cylinder. Therefore,

Total Surface Area,

TSA=2\pi r (r+h)

TSA=2\times \frac{22}{7} \times 0.14 (0.14 + 2)

TSA=1.88 m^2

Therefore, the amount of sheet required for making the closed cylindrical tank is 1.88 m^2

### 3. A metal pipe is 49 cm long. The inner diameter of cross-section is 5 cm, the outer diameter being 5.5 cm, find its,

### i. Inner Curved Surface Area

ii. Outer Curved Surface Area

iii. Total Surface Area

**Solution:**Given,

Height of the metal, h=49 cm

Inner Diameter, d_1=5 cm

Outer Diameter, d_2=5.5 cm

Therefore,

Inner Radius, r_1=2.5 cm

Outer Radius, r_2=2.75 cm

i. Inner Curved Surface Area

CSA_1=2\pi r_1 h

CSA_1=2\times \frac{22}{7}\times 2.5\times 49

CSA_1=770 cm^2

ii. Outer Curved Surface Area

CSA_2= 2\pi r_2h

CSA_2=2\times \frac{22}{7}\times 2.75\times 49

CSA_2=847 cm^2

iii. Total Surface Area

TSA=2\pi r_2(r_2+h)

TSA=2\times \frac{22}{7}\times 2.75\times (2.75+49)

TSA=894.54 cm^2

### 4. The diameter of a roller is 70 cm and its length is 140 cm. It takes 600 complete revolutions to move once over to level a playground. Find the area of the playground in m2?

**Solution:**

Given,

Diameter of the Roller, D=70 cm

The Radius of the Roller will be, r= 35 cm

Height of the Roller, h=140 cm

One revolution of the roller is equal to the Curved Surface Area of the roller. Therefore,

CSA=2\pi rh

CSA=2\times \frac{22}{7}\times 35\times 140

CSA=30800 cm^2

CSA=3.08 m^2

Since the roller takes 600 revolutions to move once over to level the playground, the area of the playground will be,

A=600\times CSA of the Roller

A=600×3.08 m^2

A=1848 m^2

### 5. A Cylindrical pillar is 42 cm in diameter and 2 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 10 per m2?

**Solution:**

Given,

Diameter of the pillar, D = 42\,cm

The Radius of the pillar will be, r = 21 cm = 0.21m

Height of the Pillar, h = 2 m

The curved Surface Area of the Pillar is,

CSA=2\pi rh

CSA=2\pi \frac{22}{7} \times 0.21 \times 2

CSA=2.64 m^2

The cost of Painting per m^2 is = Rs.\,10

The cost of Painting 2.64 m^2 is

= Rs. 10 × 2.64 m^2

= Rs. 26.4

### 6. Curved Surface Area of a Right Circular Cylinder is 5 m2. If the radius of the base of the cylinder is 1.4 m. Find its height.

**Solution:**

Given,

CSA of the Cylinder= 5 m^2

The radius of the Cylinder, r=1.4 m

We know that,

CSA=2\pi rh

h=\frac{CSA}{2\pi r}

h=\frac{5}{8.8}

h=0.56m

### 7. The inner diameter of a circular well is 4.2 m. It is 10 m deep. Find

i. Its inner curved surface area

ii. The cost of plastering this curved surface area at the rate of Rs. 40 per m2.

**Solution:**Given,

Diameter of the Circular well, D=4.2 m

The Radius of the well will be, r= 2.1 m

Height of the Circular Well, h= 10 m

i. The Inner Curved Surface Area

We know that,

CSA=2\pi rh

CSA=2\times \frac{22}{7}\times 2.1\times 10

CSA=132 m^2

ii. Cost of Painting in 1 m^2 is = Rs.\, 40

Cost of Painting 132 m^2 is = Rs.\, 40\times 132= Rs.\, 5280

### 8. In a hot water heating system there is a cylindrical pipe of length 42 m and diameter 10 cm. Find the total radiating surface of the system.

**Solution:**

Given,

Diameter of the Cylindrical pipe, D= 10\,cm

The radius of the Cylindrical Pipe, r=5cm=0.05m

Height of the Cylindrical Pipe, h=42m

The total radiating surface of the system is the curved surface area of the pipe.

Therefore,

CSA=2\pi rh

CSA=2\times \frac{22}{7}\times 0.05\times 42

CSA=13.2 m^2

## Frequently Asked Questions (FAQ)

### What is TSA of cylinder?

The TSA of a Cylinder is the Total Surface Area of the cylinder that includes the area of the top and the bottom faces. The formula for finding the Total Surface Area of a Right Circular Cylinder is given by, 2πr(r+h)

### What is the formula of total surface area of a cylinder?

The formula for finding the Total Surface Area of a Cylinder is given by, 2πr(r+h)

**Related Posts**

- Curved Surface Area of Right Circular Cylinder
- Total Surface Area of Cube
- Lateral Surface Area of Cube

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