Surface Area and Volume Formulas Class 9

Surface Area Formulas

• Surface Area of a Cuboid: Calculated using the formula 2(lb + bh + hl), where l = length, b = breadth, h = height.
• Surface Area of a Cube: Given by 6a², where a is the length of one side.
• Lateral Surface Area of a Cuboid: Found using 2lh + 2bh or simplified as 2(l + b)h.
• Lateral Surface Area of a Cube: Computed as 4a², emphasizing its relationship to the sides of the cube.
• Curved Surface Area of a Cylinder: Expressed as 2πrh, involving the radius (r) and height (h) of the cylinder.

Cylinder's Total Surface Area

• Total Surface Area of a Cylinder: Calculated with 2πr(r + h) or 2πr² + 2πrh, representing both curved and circular ends.

Important Constants

• Value of π (Pi): Commonly approximated as 22/7 or 3.14, vital for calculations involving circles and curvature.

Cone Surface Area

• Curved Surface Area of a Cone: Given by πrl, where l = slant height. Alternatively expressed as 1/2 × 2πr, where l² = r² + h².
• Total Surface Area of a Cone: Formula combines curved area and base area: πrl + πr².

Sphere and Hemisphere Area

• Surface Area of a Sphere: Defined by the formula 4πr², where r is the radius.
• Curved Surface Area of a Hemisphere: Calculated as 2πr², representing half of the sphere’s curvature.
• Total Surface Area of a Hemisphere: Results in 3πr², combining the curved area and the circular base.

Volume Formulas

• Volume of a Cuboid: Determined by the product of its dimensions: length × breadth × height.
• Volume of a Cube: Found using the cube of its side length, expressed as a³.
• Volume of a Cylinder: Given by πr²h, incorporating the area of the base and the height.
• Volume of a Cone: Calculated as 1/3πr²h, indicating that it is one-third the volume of a cylinder with the same base and height.
• Volume of a Sphere: Computed using the formula 4/3πr³, a key equation in geometry.
• Volume of a Hemisphere: Found using 2/3πr³, representing half the volume of a sphere.

Circle Measurements

• Area of a Circle: Expressed as πr², crucial for understanding circular spaces.
• Circumference of a Circle: Calculated with 2πr, representing the distance around the circle.

Pipe Volume

• Volume of a Pipe: Derived with the formula πh(outer radius - inner radius), taking thickness into account.