Category : 9th Class
Surface Area and Volume
In this chapter, we will learn about some important formulas related to 2-D and 3-D geometrical shapes.
Area of a Triangle
Circle
Length of Arc and Area of a Sector
Let an arc AB an angle 0 < 180° at the center (O) of a circle a4 radius; Then we have:
Perimeter and Area of a Rectangle
Let ABCD be a rectangle in which length \[AB\text{ }=1\] units, breadth \[BC\text{ }=\text{ }b\] units then we have:
Area of Four Walls of a Room
Let I, b and h are respectively the length/ breadth and height of a room, then area of four walls of the room =\[\left\{ 2\,\left( l+b \right)\times h \right\}\text{ }sq\text{ }units.\]
Perimeter and Area of Square
Let ABCD be a square with each side equal to ?a? units, then
Area of Some Special Types of Quadrilateral
Solids
The objects having definite shape and size are called solids. A solid occupies a definite space.
Cuboid
For a cuboid of length = l, breadth = b and height = h, we have:
Cube
For a cube having each edge = a units, we have:
Cylinder
Solids like jar, circular pencils, circular pipes, road rollers, gas cylinders are of cylindrical shape. For a cylinder of base radius = r units and height = h units, we have:
Cone
Consider a cone in which base radius = r, height = h and slant height\[\left( l \right)=\sqrt{{{h}^{2}}+{{r}^{2}}}\], then we have:
Sphere
Objects like a football, a cricket ball, etc. are of spherical shapes. For a sphere of radius r, we have:
Hemisphere
A plane through the centre of a sphere cuts it into two equal parts, each part is called a hemisphere. For a hemisphere of radius r, we have:
Find the area of the triangle whose base is 25 cm and height is 10.8 cm.
(a) 125 \[c{{m}^{2}}\] (b) 135 \[c{{m}^{2}}\]
(c) 124 \[c{{m}^{2}}\] (d) 199 \[c{{m}^{2}}\]
(e) None of these
Ans. (b)
Explanation: Area of the given triangle \[=\left( \frac{1}{2}\times 25\times \text{10}\text{.8} \right)c{{m}^{2}}=135\text{ }c{{m}^{2}}\]
A chord of a circle of radius 14 cm makes a right angle at the centre. Find the area of the major sector of the circle.
(a) 590\[c{{m}^{2}}\] (b) 462\[c{{m}^{2}}\]
(c) 595\[c{{m}^{2}}\] (d) 995\[c{{m}^{2}}\]
(e) None of these
Ans. (b)
Explanation: Area of the major sector \[\frac{270}{360{}^\circ }\times \pi {{r}^{2}}\]
= \[\frac{270{}^\circ }{360{}^\circ }\times \frac{22}{7}\times 14\times 14=462\text{ c}{{\text{m}}^{\text{2}}}\]
The length of a rectangular plot of land is twice its breadth. If the perimeter of the plot is 210 m, then find its area.
(a) 2450\[{{m}^{2}}\] (b) 2251\[{{m}^{2}}\]
(c) 5560\[{{m}^{2}}\] (d) 9060\[{{m}^{2}}\]
(e) None of these
Ans. (a)
Explanation: Let x metre be the breadth of the triangle, then its length will be 2x metre.
Now, \[2(x+2x)=210\Rightarrow \text{ }x=35\]
\[Area=35\times 70=2450\text{ }{{m}^{2}}\]
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