Surface area and Volume Class 9 All Formulas
In Class 9 mathematics, surface area and volume are fundamental concepts that delve into the measurement of three-dimensional objects. Students explore various shapes and their respective formulas to calculate surface area and volume. The curriculum covers essential geometric shapes like cubes, cuboids, cylinders, cones, spheres, and more.
For surface area, learners encounter formulas tailored to each shape, including lateral and total surface area calculations. Volume formulas offer insights into the spatial capacity of these objects. Understanding these concepts aids in solving real-life problems related to packing, construction, and designing.
By mastering surface area and volume formulas, students develop a solid foundation in geometry, paving the way for more advanced mathematical concepts in higher grades.
Right Circular Cone
Curved Surface Area of a Cone = 1/2 × l × 2πr = πrl
Total Surface Area of a Cone = πrl + πr2 = πr(l + r)
Volume of Cone = 1/3 πr2h
Sphere
Surface Area of a Sphere = 4 π r2
Curved Surface Area of a Hemisphere = 2πr2
Total Surface Area of a Hemisphere = 3πr2
Volume of a Sphere = 4/3 π r3
Volume of a Hemisphere = 2/3 πr3
Square
The formulas for a square, a two-dimensional geometric shape, are as follows:
Perimeter of a square (P): P = 4 * side length (s)
The perimeter is the sum of all four sides of the square.
Area of a square (A): A = side length (s) * side length (s) or A = s2
The area is the measure of the space enclosed within the square. It is calculated by multiplying the length of one side by itself (squared).
Rectangle
For a rectangle, another two-dimensional geometric shape, the formulas are as follows:
Perimeter of a rectangle (P): P = 2 * (length + width)
The perimeter is the sum of all four sides of the rectangle, which can be calculated by adding the lengths of its two pairs of opposite sides.
Area of a rectangle (A): A = length * width
The area is the measure of the space enclosed within the rectangle. It is calculated by multiplying the length by the width of the rectangle.
In a rectangle, opposite sides are equal in length and each angle measures 90 degrees (a right angle).
Volume and Capacity
Volume refers to the amount of space an object occupies, representing the three-dimensional extent it fills. On the other hand, capacity denotes the volume of material or substance that an object’s interior can hold. Both volume and capacity are measured using cubic units, providing a standard measurement for the amount of space occupied or substance accommodated within the object. This common unit of measurement facilitates precise quantification and comparison of volumes and capacities across various objects, enabling us to better understand their spatial and storage characteristics.