What is cylinder?
In mathematics, you are familiar with this figure. It is called cylinder. You have to seen the LPG gas cylinder in real life example. Here we will learn about its definition, properties, formulas, some important terms. Apart from this figure, we will learn Sphere, Cone etc. Cylinder Sphere Cone
As shown in above figure, Cylinder is a three dimensional figure. It has two parallel circular base, one at the top and other at the base. A line segment is joined by the center of two circular base is known as the axis of the cylinder. The two circular base are joined by a curved surface at fixed distance from the centre is known as the height of cylinder. The distance between centre of cylinder and curved surface is known as the radius of cylinder. Cylinder Sphere Cone
Definition of Cylinder:
A cylinder is a three dimensional solid figure that holds two circular parallel bases joined by a curved surface at a fixed distance. The center of two circular bases are joined by a line segment is known as the axis of the cylinder. The perpendicular distance between two parallel circular bases is known as the height ‘h’ and the distance between axis of the cylinder and curved surface is known as the radius of cylinder ‘r’.
Area of Cylinder:
The side view of the cylinder looks like a rectangle and the top view of the cylinder looks like a circle. Now it is easy to find the area of cylinder just like a rectangle. The length of rectangle is ‘2πr’ and the width is ‘h’.
Curved Surface Area of cylinder:
= Length x width
= 2πr x h
= 2πrh m2.
| Curved Surface Area of cylinder = 2πrh m2. |
Total Surface Area of Cylinder:
The total surface area of the cylinder is the sum of the area of curved surface and the two parallel circular bases.
Total surface area of cylinder:
= Curved surface area + Area of circular bases
= 2πrh + 2πr2
= 2πr(h + r) m2.
| Total surface area of cylinder = 2πr(h + r) m2. |
Volume of Cylinder:
The volume of cylinder is the space occupied inside the cylinder. The amount of liquid is stored in it is known as the volume. It is measured in cm3, m3, ml and litre. The volume of cylinder is three dimensional like length, width and height. The length and width gives area and The area and height gives the Volume. Hence, The volume of cylinder is the product of Area and Height. Cylinder Sphere Cone
Volume of Cylinder:
= Area of circular base x Height
= πr2 x h
= πr2h m3
| Volume of Cylinder = πr2h m3 |
Hollow Cylinder:
Area of Hollow cylinder:
As shown in above figure, R is the outer radius and r is the inner radius of cylinder. ‘h’ is the height of cylinder.
| Surface Area of outer cylinder = 2πRh |
| Surface Area of inner cylinder = 2πrh |
| Area of outer circle = πR2 |
| Area of inner circle = πr2 |
Area of Thickness circle:
= πR2 – πr2
= π (R2 – r2)
| Area of Thickness circle = π (R2 – r2) |
Total surface area of cylinder:
= 2πRh + 2πrh + 2 π (R2 – r2)
= 2π (Rh + rh + R2 – r2)
= 2π {(R(h+ R) + r(h – r)}
| Total surface area of cylinder = 2π {(R(h+ R) + r(h – r)} |
Volume of Hollow cylinder:
As shown in above figure, R is the outer radius and r is the inner radius of cylinder. ‘h’ is the height of cylinder.
| Volume of outer cylinder = πR2h |
| Volume of inner cylinder = πr2h |
| Exact Volume of cylinder = π(R2 – r2)h |
What is sphere?
In mathematics, you are familiar with this figure. It is called sphere. You have to seen the football in real life example. Here we will learn about its definition, properties, formulas, some important terms. Apart from this figure, we will learn Cone. Cylinder Sphere Cone
As shown in above figure, sphere is a three dimensional figure. A circle rotates about its diameter three dimensionally, we get a sphere looks like the above figure. It doesn’t have any vertex, edges, face and angles like other 3D shapes. Its top view and side view are a circle.
Definition of Sphere:
Sphere is a three dimensional figure in round shape. The points on the surface of sphere are at equidistant from its center. The distance between the center and its surface are equal at any point on the surface is known as the radius of sphere. Example: Globe, Football etc.
Surface Area of Sphere:
Total area covered by the surface of a sphere in three dimensional space is known as the surface area of sphere.
| The surface area of sphere = 4πr2 m2. |
Volume of Sphere:
The space occupied by the sphere three dimensionally is known as the volume of sphere. As shown in above figure.
| Volume of Sphere = 4/3 πr3 m3. |
What is Cone?
In mathematics, you are familiar with this figure. It is called cone. You have to seen the ice-cream cone in real life example. Here we will learn about its definition, properties, formulas, some important terms. Cylinder Sphere Cone
In mathematics, A cone is a three dimensional figure. A circular base at the bottom and a vertex at the top. The distance between the center of circular base and the vertex is known as the height of cone ‘h’. A line segment drawn from a point on the circumference of circular base to the vertex is called Slant height ‘l’. The radius of circular base is ‘r’. Its top view is a circle and side view is a triangle.
Definition of Cone:
The surface traced by a fixed moving line segment around a fixed point vertex and form a circular base of radius ‘r’. The line passes through the center of circular base and the vertex is known as the axis of the cone.
Slant Height of Cone:
Let a cone of radius ‘r’ and vertical height ‘h’ with a circular base at the bottom and a vertex at the top of cone. Slant height is derived by the Pythagoras Theorem.
| Slant Height l = √(r2+h2) |
Lateral surface area of cone:
The lateral surface area of the cone is covered by the curved surface with the slant height of cone. As shown in above figure.
| Lateral surface area of cone = πrl m2. |
Area of circular base of cone:
Area of circular base of the cone is covered by the circle at the bottom of cone with radius ‘r’. As shown in above figure.
| Area of circular base = πr2 m2. |
Total surface area of cone:
Total surface area of a right circular cone is the sum of its lateral surface area and the area of circular base of the cone.
Total surface area of cone:
= Area of lateral surface + Area of base
= πrl + πr2
= πr(l + r) m2
| Total surface area of cone = πr(l + r) m2 |
Volume of the cone:
The volume of a cone is a space occupied inside the cone with the radius ‘r’, slant height ‘l’ and height ‘h’ and vertex. The liquid is stored in it is called the volume.
| Volume of the cone = 1/3 πr2h cubic units |
Types of Cone:
# Right Circular Cone
# Oblique Cone
Right Circular Cone:
Right circular cone is a such type of cone in which a line segment is drawn perpendicularly from the vertex to the center of the circular base of cone.
Oblique Cone:
Oblique cone is such type of cone in which a line segment is drawn perpendicularly from the vertex to the base of cone except the center of the circular base of a cone. We can say that a line segment is not drawn perpendicularly from the vertex to the center of the circular base of the cone.
Frustum of Right Circular Cone
Frustum is a cutting piece of a cone in which a manner that the base of the cone and the plane of cutting are parallel to each other.
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