DIGITAL TEXT BOOK

MATHEMATICS Presented by Divya Raj BEd Mathematics 18021384004 SVMCTE,Vendar

MATHEMATICS Standard IX

Content Different bases Volume Area Cylinder

PRISM

Different Bases We have learnt about rectangular blocks and their volumes in class 6. Its outer surface is made up of many rectangles: two identical rectangles at the top and bottom, two on the left and right a third pair at the front and back, making six rectangles in all.

These all pictures have sandal spreads and vertical heights. They are Solids , also called three dimensional objects. The surface of any of them is made up of to identical polygons and rectangles of the same height, with the polygons as opposite sides. Such solids are collectively called Prisms.

The polygons and rectangles in a prism are called it's faces. The polygons on the top and the bottom are called a bases and rectangles are colour lateral faces. Depending on the shape of the bases, prisms can be classified as triangular prisms, quadrangular prisms and so on.

Volume The volume of any prism is the product of its base area and height. Activity -1 Q.If the base of a prism is an equilateral triangle of side 4 cm and its height is 10 cm then ,find its volume

AREA The lateral surface area of any prism is the product of the base perimeter and height. ACTIVITY-2 Lateral surface area of a wooden prism of base and equilateral

triangle is 48 square centimetres, and its height is 4 cm. Six of this are put together to make a hexagonal prism. To cover it completely with coloured paper, how much paper do we need? We want the total surface area of the hexagonal prism. For that, we must add the lateral surface area and the base areas. To calculate the lateral surface area, we need the perimeter of the hexagon; and so that we have to calculate the sides of a triangle. For any prism, the lateral surface area divided by the height gives the base perimeter. Show the base perimeter of the base of a triangular prism in the problem is 48÷4=12 centimetres.

√3) square centimetres. If we take 1.73 as an approximate for √3, we can see this to be a little more than 179 square centimetres. Anyway 180 is square centimetres of paper would be enough.

Cylinder Prisms are solids with equal polygons at a two ends and rectangles all around. There are solids with a circle at both ends and smoothly curving surface all around. Such a solid is called a cylinder. Volume of the cylinder is the product of its base area and height.

ACTIVITY-3 The base of a rectangular block of wood is a square of side 10 cm and its height is 20 cm. What is the volume of the largest cylinder that can be craved out of this?

CURVED SURFACE The curved surface area of a cylinder is the product of the perimeter and height. ACTIVITY -4 The base area and the curved surface area of a cylinder are equal .What is the ratio of the base radius and height?

LEARNING OUTCOME Recall the information about polygon. Describe the peculiarities of polygon . Organise different elements to fit the situation . Interpret the concept of base area of polygon. Perform arithmetic and geometrical skills.