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Class 10 Maths: Mensuration Formulas and Applications

Explore the important mensuration formulas and their applications in Class 10 Maths, covering 2D and 3D shapes such as circles, rectangles, triangles, squares, cubes, cones, cylinders, and spheres. Learn how mensuration is applied in daily life for construction, packaging, painting, and space planning.

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Questions and Answers

What is the lateral surface area of a cylinder with radius 'r' and height 'h'?

$$2πrh$$

Which shape has a volume given by the formula $$4πr^3$$?

Sphere

In which real-life situation would mensuration be used to determine the optimal dimensions of a product for packaging or shipping?

Calculating the size of materials for construction projects

What is the total surface area of a sphere with radius 'r'?

<p>$$4πr^2$$</p> Signup and view all the answers

What is the volume of a cylinder with radius 'r' and height 'h'?

<p>$$2πrh + 2πr^2$$</p> Signup and view all the answers

What is the correct formula for the area of a parallelogram?

<p>$b \times h$</p> Signup and view all the answers

Which formula represents the volume of a cuboid?

<p>$2(l + b + h)$</p> Signup and view all the answers

What is the perimeter formula for a trapezium?

<p>$a + b + c$</p> Signup and view all the answers

Which of the following represents the lateral surface area of a cube?

<p>$6a^2$</p> Signup and view all the answers

What is the correct formula for the lateral surface area of a cone?

<p>$\pi r(l + h)$</p> Signup and view all the answers

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Study Notes

Mensuration in Class 10 Maths

Mensuration is a branch of mathematics that deals with the measurement of geometric figures, their volume, shape, and surface area. In Class 10 Maths, the mensuration chapter focuses on the applications of formulas for various 2D and 3D shapes, including circles, rectangles, triangles, squares, and cubes. This article will discuss the important formulas and their applications in mensuration, particularly in the context of Class 10 Maths.

Important Mensuration Formulas for Class 10 Maths

Some of the key mensuration formulas for Class 10 Maths are as follows:

  1. Circle:

    • Area: $$πr^2$$
    • Perimeter (or Circumference): $$2πr$$
  2. Square:

    • Area: $$a^2$$
    • Perimeter: $$4a$$
  3. Rectangle:

    • Area: $$l × b$$
    • Perimeter: $$2(l + b)$$
  4. Triangle:

    • Area: $$\frac{1}{2} × height × base$$
    • Perimeter: $$a + b + c$$
  5. Parallelogram:

    • Area: $$b × h$$
    • Perimeter: $$2(l + b)$$
  6. Rhombus:

    • Area: $$\frac{1}{2} × d1 × d2$$
    • Perimeter: $$4 × side$$
  7. Trapezium:

    • Area: $$\frac{1}{2} × h(a + b)$$
    • Perimeter: $$a + b + c$$
  8. Cube:

    • Volume: $$a^3$$
    • Lateral Surface Area: $$6a^2$$
  9. Cuboid:

    • Volume: $$2(l + b + h)$$
    • Lateral Surface Area: $$2(l + b)$$
  10. Cone:

    • Volume: $$\frac{1}{3} × πr^2h$$
    • Lateral Surface Area: $$πr(l + h)$$
  11. Cylinder:

    • Volume: $$2πrh + 2πr^2$$
    • Lateral Surface Area: $$2πrh$$
  12. Sphere:

    • Volume: $$4πr^3$$
    • Lateral Surface Area: $$4πr^2$$

These formulas are used to solve various problems in Class 10 Maths chapters, such as determining the area, perimeter, volume, and lateral surface area of different shapes.

Applications of Mensuration in Daily Life

Mensuration is applied in our daily lives in various ways, such as:

  • Calculating the size of the required materials for construction projects
  • Determining the optimal dimensions of a product for packaging or shipping
  • Estimating the volume of paint needed for painting a wall or object
  • Planning the layout of furniture in a room or public space

In conclusion, mensuration is an essential topic in Class 10 Maths, as it helps students understand the measurement of geometric figures and their applications in real-life situations. By learning and practicing these formulas, students can develop a strong foundation in mensuration and apply it to various problems in their daily lives.

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