Nios Class 10 Maths Practical

 Most Important 4 Practicals for NIOS Class 10 Mathematics

1. Verification of the Pythagoras Theorem

Objective:

To verify the Pythagoras theorem using a right-angled triangle.

Procedure:

1. Draw a right-angled triangle on a cardboard or graph paper with sides labeled as a, b, and c, where c is the hypotenuse.

2. Measure the lengths of all three sides using a ruler.

3. Calculate the squares of the two smaller sides, a² and b².

4. Calculate the square of the hypotenuse, c².

5. Compare whether a² + b² = c² holds true.

6. Repeat with different sets of right-angled triangles for verification.

Expected Output:

The sum of the squares of the two shorter sides should be equal to the square of the hypotenuse, proving the Pythagoras theorem.

2. Construction of a Circumcircle of a Triangle

Objective:

To construct a circumcircle of a given triangle using a compass and ruler.

Procedure:

1. Draw any triangle ABC on a sheet of paper.

2. Construct the perpendicular bisectors of any two sides (e.g., AB and BC).

3. Mark the point where these bisectors intersect as O (circumcenter).

4. Place the compass at O and adjust it to reach any one of the triangle's vertices.

5. Draw a circle with radius OA, which should pass through all three vertices of the triangle.

6. Verify that the circle passes through A, B, and C.

Expected Output:

A triangle inscribed within a circle, with the circle passing through all three vertices, proving it as the circumcircle.

 3. Verification of the Midpoint Theorem

Objective:

To verify the midpoint theorem, which states that the line joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.

Procedure:

1. Draw a triangle ABC on a sheet of paper.

2. Find the midpoints of two sides, D (midpoint of AB) and E (midpoint of AC).

3. Draw the line segment DE joining these midpoints.

4. Measure DE and BC using a ruler.

5. Compare the length of DE with BC (DE should be half of BC).

6. Check whether DE is parallel to BC using a set square.

Expected Output:

The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length, confirming the midpoint theorem.

4. Finding the Surface Area and Volume of a Cylinder

Objective:

To calculate the surface area and volume of a cylindrical object using real measurements.

Procedure:

1. Take any cylindrical object like a water bottle or a tin can.

2. Measure its radius (r) and height (h) using a measuring tape.

3. Calculate the curved surface area using the formula:

4. Calculate the total surface area using the formula:

5. Calculate the volume using the formula:

6. Verify calculations by substituting the values into the formulas and solving them.

Expected Output:

Accurate calculations of the curved surface area, total surface area, and volume of the cylindrical object, reinforcing the concept of mensuration.