Right Circular Cylinder in Geometry
A right circular cylinder is a three-dimensional geometric shape composed of two circular bases connected by a curved surface. In geometry, a right cylinder is a cylinder in which the two bases are perpendicular to the cylinder's axis and the height of the cylinder is equal to the distance between the two bases. The radius of the circular bases is the same and the height of the cylinder is the same as the distance between the two bases.
Formula for Calculating the Volume of a Right Circular Cylinder
The formula for calculating the volume of a right circular cylinder is V = pr2h, where r is the radius of the circular base and h is the height of the cylinder.
For example, if the radius of the circular base is 4 cm and the height of the cylinder is 10 cm, then the volume of the right circular cylinder is V = p(4)2(10) = 502.65 cm3.
Formula for Calculating the Surface Area of a Right Circular Cylinder
The formula for calculating the surface area of a right circular cylinder is SA = 2pr2 + 2prh, where r is the radius of the circular base and h is the height of the cylinder.
For example, if the radius of the circular base is 4 cm and the height of the cylinder is 10 cm, then the surface area of the right circular cylinder is SA = 2p(4)2 + 2p(4)(10) = 232 cm2.
Circumference of a Right Circular Cylinder
The circumference of a right circular cylinder is the perimeter of the two circular bases. The formula for calculating the circumference of a right circular cylinder is C = 2pr, where r is the radius of the circular base.
For example, if the radius of the circular base is 4 cm, then the circumference of the right circular cylinder is C = 2p(4) = 25.13 cm.
Practice Problems with Answers
1. Calculate the volume of a right circular cylinder with a radius of 3 cm and a height of 12 cm.
Answer: V = p(3)2(12) = 282.74 cm3.
2. Calculate the surface area of a right circular cylinder with a radius of 5 cm and a height of 8 cm.
Answer: SA = 2p(5)2 + 2p(5)(8) = 314 cm2.
3. Calculate the circumference of a right circular cylinder with a radius of 7 cm.
Answer: C = 2p(7) = 43.98 cm.
4. Calculate the volume of a right circular cylinder with a radius of 8 cm and a height of 6 cm.
Answer: V = p(8)2(6) = 904.78 cm3.
5. Calculate the surface area of a right circular cylinder with a radius of 9 cm and a height of 4 cm.
Answer: SA = 2p(9)2 + 2p(9)(4) = 376 cm2.
6. Calculate the circumference of a right circular cylinder with a radius of 10 cm.
Answer: C = 2p(10) = 62.83 cm.
Summary
A right circular cylinder is a three-dimensional geometric shape composed of two circular bases connected by a curved surface. The formula for calculating the volume of a right circular cylinder is V = pr2h, where r is the radius of the circular base and h is the height of the cylinder. The formula for calculating the surface area of a right circular cylinder is SA = 2pr2 + 2prh, where r is the radius of the circular base and h is the height of the cylinder. The circumference of a right circular cylinder is the perimeter of the two circular bases and the formula for calculating the circumference of a right circular cylinder is C = 2pr, where r is the radius of the circular base.
FAQ
See more Dies Backstage At Theatre ...What are the properties of a right circular cylinder?
A right circular cylinder is a three-dimensional solid figure. It is a type of cylinder having a closed circular surface on both ends, with the axis of the cylinder joining the two centers of the bases perpendicular to the bases. The total surface area of the cylinder is 2p (h + r). Examples of right circular cylinders include pipes, cans, and paper towel rolls.
Why is cylinder called right circular cylinder?
A right circular cylinder is called so because the axis of the cylinder is perpendicular to the bases. The bases of the cylinder have the same radius and are parallel to each other.
How is a right circular cylinder formed?
A right circular cylinder is formed by taking a rectangle and rolling it up or by connecting two circles of the same radius with a curved surface.
What is the formula for the surface area of a right circular cylinder?
The formula for the surface area of a right circular cylinder is 2p (h + r), where h is the height of the cylinder and r is the radius of the base.
What is the difference between a cylinder and a right circular cylinder?
A cylinder is a three-dimensional figure with two circular bases, while a right circular cylinder is a type of cylinder having a closed circular surface on both ends, with the axis of the cylinder joining the two centers of the bases perpendicular to the bases. All the points of a right circular cylinder are the same distance from the axis.
What is a Right Circular Cylinder Shape?
A right circular cylinder is a three-dimensional solid figure. It is a type of cylinder having a closed circular surface on both ends, with the axis of the cylinder joining the two centers of the bases perpendicular to the bases. The total surface area of the cylinder is 2p (h + r). Examples of right circular cylinders include pipes, cans, and paper towel rolls.
What are the Real-Life Examples of Right Circular Cylinder?
Examples of right circular cylinders include pipes, cans, and paper towel rolls.
How many sides does a right circular cylinder have?
A right circular cylinder has two circular bases and one curved side.
What is a right circular cylinder?
A right circular cylinder is a three-dimensional solid figure. It is a type of cylinder having a closed circular surface on both ends, with the axis of the cylinder joining the two centers of the bases perpendicular to the bases. The total surface area of the cylinder is 2p (h + r). Examples of right circular cylinders include pipes, cans, and paper towel rolls.