Making a right circular cylinder

Aim To make a right circular cylinder of given height and circumference of base. To calculate the curved surface area and the total surface area. Material required Coloured paper, pair of scissors , cello tape and geometry box.

Procedure Step 1 Let the circumference of base =22 cm and height of cylinder =10 cm. Step2 Cut a rectangle of length equal to the circumference of base (22 cm ) and breadth equal height of cylinder(10 cm). Step3 Gently curve the paper so that the two shorter sides come closer , put a cello tape. Step4 To make the top and base of cylinder ,firstly calculate the radius of the base and the top circles. 2 X Pi X r = 22 2 X 22/7 X r = 22 , r=7/2

r=3.5 cm.

Step5 Cut 2 circles of radii 3.5 cm each. Step 6 Cover the base and the top of the cylinder with the circles using a cello tape. Step7 Calculate the curved surface area by removing top and base circles. Curved surface area of cylinder =area of rectangle =lenght *breadth = 2 Pi r * h = 2 Pi r h = 22*10 = 220 cm sq. Total surface area = area of rectangle + 2[area of circle] =2 pi r h +2[pi r*r] =220 + 2[22/7 * 7/2 * 7/2] =220 + 77 =297 cm sq Observations The rectangle transforms into a cylinder. The height of the cylinder is breadth of the rectangle. The circumference of the base of the cylinder is the length of the rectangle.

Diameter is the longest chord

Aim By paper folding verify the result "Diameter is the longest chord of a circle" Material Required Coloured Paper, pair of scissors, fevistick, ruler , sketch pen Procedure Step 1. Draw a circle of any radius on a coloured paper and cut it. Step 2. Fold the circle cut out in any way , a crease is formed. Step 3. On the crease draw a chord AB. Step 4. Similarly get another chord CD. Step 5. To get the diameter of the circle, fold the circle in such a way that the crease passes through the centre of the circle. Label the diameter as PQ. Step 6. Measure the lengths of AB,CD and PQ. Step 7. Write the observations. Result On comparing the length of diameter and other chords, it is observed that diameter is the longest chord.

Activity- Vertically opposite angles are equal

Aim To verify by paper cutting and pasting,the vertically opposite angles are equal. Material required: Coloured paper, carbon paper, ruler, pencil, pair of scissors, glue Procedure: Step1 : On a sheet of paper draw two intersecting lines AB and CD. Let the two lines intersect at O. Step 2: Label the two pairs of vertically opposite angles as angle1 opposite to angle 2 and angle 3 opposite to angle 4. Step 3: Make the replica of angle 2 and angle 3 and cut it. Step 4: Place the cut out of angle 2 on angle 1. Are they equal? Step 5: Place the cut out of angle 3 on angle 4. Are they equal? Write your observations and result.

Basic Proportionality Theorem

Aim To verify the Basic Proportionality theorem by paper cutting and pasting using a parallel line board.
Material required Coloured paper, parallel line board, pair of scissors, sketch pen, ruler, glue

Procedure
Step 1 Draw a triangle on a coloured paper.
Step 2 Label the triangle as ABC.
Step 3 Cut the triangle.
Step 4 Take the parallel line board and place the triangle ABC on it such that the side BC coincides with any of lines on the board.
Step 5 Draw a line parallel to BC using a ruler by the help of lines on the parallel line board.
Step 6. Let the parallel line drawn to BC intersect AB and AC at D and E respectively.
Step 7. Find AD/DB and AE/EC.
Step 8. What do you observe?
Step 9. Repeat the activity for two more triangles.
Step 10. Write the result.

If a line is drawn parallel to any side of a triangle,to intersect the other two sides at two distinct points,then the other two sides are divided in the same ratio.