Understanding the surface area and volume of a right circular cylinder is essential for solving various geometric problems. In this article, we learn about an important topic of class 9 Surface Area and Volume of a Right Circular Cylinder.
This article will provide a clear understanding of the right circular Cylinder and surface area and volume of a right circular cone, along with some Surface Area and Volume of a Right Circular Cylinder problems to reinforce your understanding.
Right Circular cylinder
Right circular cylinder is a 3D shape with two parallel circular bases connected by a curved surface. The line connecting the centers of the bases is perpendicular to the bases and is called the axis. The height (h) is the distance between the bases, and the radius (r) is the radius of the circles.
Formulas for Surface Area and Volume of a Right Circular Cylinder
Various important formulas related to Surface Area and Volume of a Right Circular Cylinder Problem are added in the table below:
CSA = (Perimeter of Circular ends)×height(h) = | |
Total Surface Area of Right-Circular Cylinder | TSA = Lateral Surface Area + 2×(Area of Circle) = |
Volume = |
where,
- r is Radius of Cylinder
- h is Height of Cylinder
Surface Area and Volume of a Right Circular Cylinder Problems - Unsolved
Q1. Find the surface area of a cylinder with radius r = 4 cm and height ℎ= 8cm.
Q2. A cylindrіcal tank has a radius of 5 meters and a height of 10 meters. Calculate іts total surface area.
Q3. If the diameter of a cylindrіcal contaіner іs 12 іnches and іts heіght іs 15 іnches, fіnd іts total surface area.
Q4. A cylindrіcal pіllar has a heіght of 20 feet and a circumference of 12 feet. Determіne іts surface area.
Q5. A cylindrіcal tube has a radius of 3 cm and a heіght of 15 cm. Calculate іts total surface area.
Q6. Surface area of a cylindrіcal contaіner іs 400 square meters, and іts heіght іs 10 meters. Fіnd іts radius.
Q7. A cylindrіcal contaіner has a heіght of 12 іnches, and іts total surface area іs 150 square іnches. Determіne іts radius.
Q8. Calculate the volume of a cylindrіcal tank wіth a radius of 6 meters and a heіght of 10 meters.
Q9. If the diameter of a cylindrіcal pіpe іs 8 cm and іts length іs 20 cm, fіnd іts volume.
Q10. A cylindrіcal contaіner has a volume of 1000 cubіc centіmeters, and іts heіght іs 20 centіmeters. Determіne іts radius.
Surface Area and Volume of a Right Circular Cylinder Problems - Solved
1: Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m. Find its height.
Given,
- Radius of the base of the cylinder = r = 0.7 m
- Curved surface area of cylinder = C.S.A = 4.4m2
Let ‘h’ be the height of the cylinder.
We know, curved surface area of a cylinder = 2πrh
Therefore,
2πrh = 4.4
2 × 3.14 × 0.7 × h = 4.4 [using π=3.14]
h = 1
Therefore the height of the cylinder is 1 m.
2: It is required to make a closed cylindrical tank of height 1 m and the base diameter of 140 cm from a metal sheet. How many square meters of the sheet are required for the same?
Height of cylindrical tank (h) = 1 m
Base radius of cylindrical tank (r) = diameter/2
r = 140/2 cm
r = 70 cm = 0.7 m [1 m = 100 cm]
Now,
Area of Sheeet Required = Total Surface Area of Tank (TSA) = 2πr(h + r)
= 2 × 3.14 × 0.7(1 + 0.7)
= 7.48
Therefore, 7.48 m2 metal sheeet is required to make required closed cylindrical tank.
3: Find the ratio betweeen the total surface area of a cylinder to its curved surface area, given that height and radius of the tank are 7.5 m and 3.5 m.
- Height of cylinder (h) = 7.5 m
- Radius of cylinder (r) = 3.5 m
We know,
- Total Surface Area of cylinder (T.S.A) = 2πr(r+h)
- Curved Surface Area of a Cylinder(C.S.A) = 2πrh
Now, Ratio between the total surface area of a cylinder to its curved surface area is
T.S.A/C.S.A = 2πr(r+h)/2πrh
= (r + h)/h
= (3.5 + 7.5)/7.5
= 11/7.5
= 22/15 or 22:15
Therefore the required ratio is 22:15
4: Inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 gm.
Let r and R be the inner and outer radii of cylindrical pipe.
Inner radius of a cylindrical pipe (r) = 24/2 = 12 cm
Outer radius of a cylindrical pipe (R) = 24/2 = 14 cm
Height of pipe (h) = length of pipe = 35 cm
Mass of pipe = volume × density = π(R2 – r2)h
= 22/7(142 – 122)35
= 5720
Mass of pipe is 5720 cm3
Mass of 1 cm3 wood = 0.6 gm (Given)
Therefore, mass of 5720 cm3 wood = 5720 × 0.6 = 3432 gm = 3.432 kg
5: If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, find:
i) radius of its base (ii) volume of the cylinder
[use π = 3.141]
Lateral Surface of Cylinder = 94.2 cm2
Height of Cylinder = 5 cm
Let ‘r’ be the radius
(i) Lateral Surface of Cylinder = 94.2 cm2
2πrh = 94.2
2 × 3.14 × r × 5 = 94.2
r = 3 cm
(ii) Volume of the cylinder = πr2h
= (3.14 × 32 × 5) cm3
= 141.3 cm3
6: A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
Radius of Cylindrical Bowl (R) = diameter/2 = 7/2 cm = 3.5 cm
Height = 4 cm
Now,
Volume of Soup in 1 bowl = πr2h
= 22/7×3.52×4 cm3
= 154 cm3
Volume of Soup in 250 bowls = (250 × 154) cm3
= 38500 cm3
= 38.5 liters
Thus, hospital has to prepare 38.5 liters of soup daily in order to serve 250 patients.
7: Cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corrected to 2 decimal places.
Let ‘r’ be the radius of the tank
Given,
Height (h) = 6(Radius) = 6r dm
Cost of painting for 50 paisa or Rs 1/2 per dm2 = Rs 198 (Given)
⇒ 2πr(r+h) × 1/2 = 198
⇒ 2×22/7×r(r+6r) × 1/2 = 198
⇒ r = 3 dm
And, h = (6 x 3) dm = 18 dm
Now,
Volume of the tank = πr2h = 22/7×9×18 = 509.14 dm3
