Page 95 - Mathematics Class - X

PROJECT 8

AIM

Extensions of Pythagoras theorem.

MATERIALS REQUIRED
Drawing sheet
Geometry box
Three containers of different radii in the shapes of right circular cylinder
Water, three more containers of different radii in the shape of right circular cone
Sand
Glazed paper
Fevistick
A pair of scissors

PROCEDURE
1. Take three right circular cylinders of same height and of different radii, say 3 cm, 4 cm and 5 cm.
2. Fill the two smaller cylinders (r = 3 cm, 4 cm) with water and keep empty the bigger cylinder of radius 5 cm.

3. Now, pour water from the two smaller cylinders (r = 3 cm, 4 cm) to the bigger cylinder (r = 5 cm).
4. We found that the bigger cylinder is completely filled with water as shown the given figure.

3 cm 4 cm 5 cm

h + h = h

RESULT
From the above procedure, we have
Volume of cylinder with radius 5 cm

= Volume of cylinder with radius 3 cm + Volume of cylinder with radius 4 cm

\ p × (5) × h = p × (3) × h + p × (4) × h [Q volume of cylinder = pr h]
2
2
2
2
⇒ (5) = (3) + (4) 2
2
2
Hence, Pythagoras theorem can be extended for right circular cylinder.
Pythagoras theorem can also be extended for right circular cone.
CONCLUSION
From the above three results, we conclude that Pythagoras theorem which is true for right triangles can be extended
to three-dimensional figures such as cylinders.

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