In this chapter we will solve questions related to lateral and total surface area of cylinder.

Given below are the formulas for area calculation for cylinder with radius r and height h.

**Lateral surface area**

The area of the curved surface of cylinder is called lateral surface area.**Lateral surface area = 2.𝜋.r.h**

Lateral surface area is also known as curved surface area.

**Total surface area**

Total surface area includes the area of two bases and the curved surface area.**Total surface area = 2.𝜋.r ( h + r )**

## Surface area of cylinder – Solved problems

**Question 01**

For the cylinder with height 25 cm and radius 14 cm, find the total and curved surface area.

**Solution****Curved surface area = 2.𝜋.r.h**

Putting the values;

Curved surface area = \mathtt{2\times \frac{22}{7} \times 14\times 25\ =2200\ cm^{2}}

Hence, the **cylinder has 2200 sq cm of curved surface area**.

**Total surface area = 2.𝜋.r ( h + r ) **

Putting the values;

Total surface area = \mathtt{\ 2\times \frac{22}{7} \times 14\ ( 14+25) \ =3432\ cm^{2}}

Hence, the **cylinder has total surface area of 3432 sq cm**.

**Question 02**

If the radius and curved surface area of right circular cylinder is 2 meter and 66 sq. meter. Then calculate the height of cylinder.

**Solution**

Radius = 2 meter

Curved surface area = 66 sq. meter

Curved surface area = 2.𝜋.r.h

Putting the values;

\mathtt{66\ =\ 2\times \frac{22}{7} \times 2\times h}\\\ \\ \mathtt{h=\ \frac{21}{4} \ =5.25\ meter}

Hence, **the height of cylinder is 5.25 meter**.

**Question 03**

John want to paint the curved surface of cylindrical pillar in front of his house. The cylindrical pillar is 0.5 meter in radius and 14 meter in height. If the cost of painting is 7$ per square meter .Find the total money paise by John

**Solution**

Radius (r) = 0.5 meter

height (h) = 14 meter

Curved surface area = 2.𝜋.r.h

Putting the values;

\mathtt{Curved\ surface\ area\ =\ \ 2\times \frac{22}{7} \times 0.5\times 14\ =44\ m^{2}}

Hence,** total of 44 sq meter of area is to be painted.**

Now let’s calculate the cost to paint the pillar.

1 sq. meter cost ⟹ 7

44 sq. meter cost ⟹ 7 x 44 = 308$

Hence, **John have to pay total of 308 dollars**.

**Question 04**

A blacksmith want to build a hollow cylinder of diameter 2 meter and height 4 meter from a metal sheet. Find the area of metal sheet needed to build the cylinder.

**Solution**

Diameter = 2 meter

Radius = 1 meter

Height = 4 meter

Calculating the total surface area;**TSA = 2.𝜋.r ( h + r ) **

Putting the values;

\mathtt{TSA\ =\ 2\times \frac{22}{7} \times 1\times ( 4+1) =31.43\ sq\ meter}

Hence, **31.43 sq. meter of metal sheet is needed** to build the required cylinder.

**Question 05**

Find the ratio of total to curved surface area of cylinder if radius is 60 cm and height is 3 meters.

**Solution**

Radius = 60 cm = 0.6 meter

Height = 3 meter

TSA = 2.𝜋.r ( h + r )

CSA = 2.𝜋.r. h

Taking ratio of TSA and CSA.

\mathtt{\frac{TSA}{CSA} =\frac{2\pi r( h+r)}{2\pi rh}}\\\ \\ \mathtt{\frac{TSA}{CSA} =\frac{( h+r)}{h}}\\\ \\ \mathtt{\frac{TSA}{CSA} =\frac{3+0.6}{3} =\frac{6}{5}}

Hence, **6 : 5 is the required ratio.**