Surface Areas and Volumes in Mathematics

Surface Areas and Volumesis a fundamental topic in geometry that deals with measuring the external and internal space of 3D (three-dimensional) shapes.

Surface Area refers to the total area that the surface of a 3D object occupies. It is usually measured in square units (e.g., cm², m²). Surface areas are calculated differently based on the shape of the object, such as cubes, cuboids, cylinders, spheres, cones, and hemispheres.

Volume is the amount of space enclosed within a 3D object. It is measured in cubic units (e.g., cm³, m³). Volume calculations help determine how much material or space an object can contain.

Understanding surface area and volume is essential in real-life applications such as packaging, construction, manufacturing, and fluid storage.

Common Formulas:

• Cube:
  • Surface Area = 6a²
  • Volume = a³
• Cuboid:
  • Surface Area = 2(lb + bh + hl)
  • Volume = l × b × h
• Cylinder:
  • Surface Area = 2πr(h + r)
  • Volume = πr²h
• Sphere:
  • Surface Area = 4πr²
  • Volume = (4/3)πr³
• Cone:
  • Surface Area = πr(l + r)
  • Volume = (1/3)πr²h
• Hemisphere:
  • Surface Area = 3πr²
  • Volume = (2/3)πr³