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.