RD Sharma Class 8 Solutions Chapter 22 - Surface Area and Volume of Right Circular Cylinder (Ex 22.2) Exercise 22.2

A three-dimensional solid figure is a right circular cylinder. It's a cylinder with a closed circular surface on both ends and two parallel bases. The right cylinder is another name for it. Surface area and volume are the two most important features of the correct cylinder. The characteristics, surface area, and volume of the right circular cylinder will be discussed in this session.

What Exactly is a Right Circular Cylinder?

A right circular cylinder is a solid object having two parallel bases joined by a closed circular surface, each shaped like a round disc. The axis of the right cylinder is a line that runs through the center or connects the centers of two circular bases. The height, "h," represents the distance between the two-cylinder bases, which is referred to as perpendicular distance. The radius of the right circular cylinder, denoted by "r," is the distance between the center and the outer limit of either of the two bases. As a result, two circles and a rectangle combine to produce a right circular cylinder. Examine the figure below, which depicts the development of the right circular cylinder.

Right Circular Cylinder’s Properties

The qualities of the right circular cylinder are as follows:

• A right circular cylinder has two curved edges, one curved surface and two flat faces, just like every other two-dimensional object.

• Cylindrical bases are always congruent with one another.

• The cylinder's size is determined by the radius of the base and the height of the cylinder.

• With the bases perfectly over each other, the axis makes a straight angle with them.

• There isn't a vertex or a precise corner on it.

• The cylinder's base and top are always similar to one another.

Right Circular Cylinder’s Surface Area

A right circular cylinder's surface area is defined as the area covered by the cylinder's surface. A right circular cylinder has two types of surface areas:

• A right circular cylinder's curved surface area is also known as the right circular cylinder's lateral surface area. It is the space between the parallel circular bases of the right circular cylinder covered by the curved surface of the cylinder.

• A right circular cylinder's total surface area is defined as the total area filled by the cylinder. Two circles plus a curved surface make up this section of the cylinder. As a result, while calculating the overall surface area of the right circular cylinder, we add the areas of two circles as well as the curved surface at the end.

The right circular cylinder's surface areas are measured in square units for both types of surface areas (m2, cm2, in2, or ft2).

Right Circular Cylinder’s Surface Area Formula

Consider a right circular cylinder with a radius of "r" and a height of "h." The surface area of right circular cylinders is calculated using the following formulas:

• Curved Surface Area (CSA) = 2πrh square units

• Total Surface Area (TSA)= Curved Surface Area + 2(Area of a circle) (as Curved Surface Area(CSA) = Circumference × Height = 2πr × h)

⇒ Total Surface Area (TSA) = 2πrh + 2πr2 = 2πr(h+r) square units.

Right Circular Cylinder’s Volume

The volume of a right circular cylinder is equal to the amount of space occupied by the cylinder. In terms of cubic units, the volume of the right circular cylinder is expressed as (m3, cm3, in3, or ft3).

Right Circular Cylinder’s Volume Formula

The volume of a right circular cylinder with height "h" and radius "r" can be calculated using the following formula:

• The volume of a cylinder = Area of a circle × height

⇒ The volume of a right circular cylinder = πr2 × h cubic units