Volume And Surface Area 4m4r5y

Preliminary Information Name of the Student Teacher: Srujana. K Subject : English Class : IX Presentation Topic : Social & Religious Movements Roll No : 329 Name of the Supervisor :Ch. Jyothi Kumari

Objectives The Students will be able to: • Compute the total and lateral surface area of a cube and a cuboid • Find the total and lateral surface area of a cylinder • Compute the volume of a cuboid and a cube • Obtain the volume of a right prism and a pyramid • Determine the volume of cylinder

Raja Ram Mohan was born in Bengal in 1772 was a great scholar of Persian and English He was studied religious philosopher like Hinduism , Islam and Christianity. He says there is only one god and that worshiping idols and making sacrifices were incorrect.

Swami Dayananda Saraswathi was a socical reformer. He rejected the orthodox ritualistic Hinduism He advocated worshipping one supreme God through simple rituals He setup Arya Samaj in 1875.

Cube

If length, breadth and height of a cube are equal then the figure is said to be a “Cube” • Total surface area of a cube = 6 a2 Sq Units • Lateral surface area of a cube = 4 a2 Sq Units

Concept of Volume

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Take a glass jar, place it a container. Fill the water in glass jar up to the its brim. Slowly drop a solid object in it. Some of the water from the jar will over flow into the container. • Take the overflowed water into measuring jar. • It gives an idea of space occupied by a solid object called “ Volume”.

Volume of Cuboid The space occupied by the cuboid is called as volume of the cuboid.

• Volume of Cuboid = area of plane region X height = lb X h • Volume of cuboid = lbh cubic units.

Volume of Cube

• Volume of Cuboid = lbh • In cube, l = b = h = a (all dimensions are same) • Volume of Cube = a x a x a = a3 Cubic Units.

Volume of right Prism • Volume of right Prism = Area of the base x height

If the base of right prism is an equilateral triangle its volume = 3 a2 x h cubic units 4

Volume of Pyramid • The picture is a square Pyramid because its base is square and height h units. • The Volume of a Pyramid = 1 of the volume of right prism 3

=

1 3

area of the base x height

=

1 3

s2 x h cubic units.

1 3

Concept of Cylinder • Cut out a rectangular paper. Paste a thick string along the line as shown in the figure. • Hold the string with your hands on either sides of a rectangle and rotate the rectangle sheet about the string as fast as you can atleast the shape will be “cylinder”.

Curved surface area of a Cylinder

• The curved shape of cylinder is in rectangle shape.

The area of rectangle = area of curved surface area of a cylinder • Length = circumference of base of radius r units. • Breadth = height of the cylinder. • Curved surface area of the cylinder = area of rectangle = length x breadth = 2∏r x h = 2 ∏ rh sq units.

Total surface area of a cylinder • Totala surface area is covered by the area of top, area of base and curved surface area. • Total surface area of cylinder = curved surface area + area of top + area of base = 2∏rh + ∏r2 + ∏r2 = 2∏rh + 2 ∏r2 = 2∏r (r+h) Total surface area of a cylinder = 2∏r (r+h)

Volume of Cylinder • If we arrange the circles with same radii over one other. We get shape of “Cylinder”. So, the volume of cylinder is covered by volume of circle with the multiple of height (h)  times. Volume of Cylinder = ∏r2 x height = ∏r2 x h = ∏r2 h

Summary • •

•

Cuboid and cube are regular prisms having 6 faces and of which 4 are lateral faces and the base and top. If l, b, h are length, breadth and height of a cuboid, then Total surface area of a cuboid = 2 (lb + bh + hl) Lateral Surface Area of Cuboid = 2h (l +b) Volume of Cuboid = lbh If l is the edge of cube, then Total surface area of a cube = 6l2 Lateral surface area of a cube = 4l2 Volume of a cube = l3 Volume of a pyramid is rd volume of a right prism if both have the same base and same height If ‘r’ is the radius of right circular cylinder with height ‘h’ then Curved surface area of a cylinder = 2∏rh Total surface area of a cylindr = 2∏r (r+h) Volume of a cylinder = ∏r2 h 1 3

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Bibliography • A text book of IX class mathematics by A.P. Govt. • A text book of ICT by Neelkamal series. • A text book of ICT by New era series. • First look of 2007 OFFICE system – Katherine Murray.