Surface area and volume of spheres

key notes :

Definition of a Sphere

• A sphere is a perfectly round 3D object where all points on its surface are equidistant from the center.
• It has no edges or vertices.

Surface Area of a Sphere

• The formula for the surface area of a sphere is:

A = 4πr²

where:

• Example Calculation:
  If the radius of a sphere is 5 cm, then the surface area is:

A = 4π (5)² = 4π (25) = 100π ≈ 314.16 cm²

Volume of a Sphere

• The formula for the volume of a sphere is:

V = 43πr³

where:

• V = volume
• r = radius
• Example Calculation:
  If the radius of a sphere is 6 cm, then the volume is:

V = 4/3π (6)³ = 4/3π (216) = 864/3π = 288π ≈ 904.32 cm³

Hemisphere (Half of a Sphere)

Surface Area of a Hemisphere:

• Curved surface area (only the curved part):

A = 2πr²

• Total surface area (curved + circular base):

A = 3πr²

Volume of a Hemisphere:

V = 2/3πr³

Applications of Surface Area and Volume

• Calculating the surface area helps in painting, wrapping, and covering spherical objects.
• Volume calculations are used in determining the capacity of spherical tanks, balloons, and balls.

Important Points to Remember

Always use the same units (cm, m, etc.) in calculations.

When solving problems, round off answers only at the final step for accuracy.

If diameter is given, radius = diameter ÷ 2.

Learn with an example

let’s practice!