Current Affairs 8th Class

Category : 8th Class

Mensuration

His chapter deals with the concept of finding the surface area and volume of the regular figures. By regular figures we mean to say the figures whose parameters are known to us. Previously we have learnt to find the perimeter and area of the rectilinear figures, but now onwards we will learn to find the area of some polygons and also discuss the surface area and volume of some solid shapes namely cuboid cube, cone and cylinder.   

Area of a Polygon                                          

Area of a given polygon can be found by dividing the given polygon into non-over lapping rectilinear figures. The area of the polygon will be equal to the sum of the areas of non-overlapping figures.

• Example:

Find the area of the polygon given below if AP = 10 cm, BP = 20 cm, CP = 50 cm, DP = 60 cm and PS = 90 cm

(a) \[4080\,c{{m}^{2}}\]           (b) \[5050\,c{{m}^{2}}\]

(c) \[6060\,c{{m}^{2}}\]           (d) \[7070\,c{{m}^{2}}\]

(e) None of these                                                    

Answer (b)                                            

Explanation: Area of the given figure    

\[=\frac{1}{2}\times 30\times 10+\frac{1}{2}\times 20\times 20+\frac{1}{2}\times 40(30+40)+\frac{1}{2}\times 40\]\[(20+60)+\frac{1}{2}\times 40\times 40\times \frac{1}{2}\times 60\times 30c{{m}^{2}}\]

\[=(150+200+1400+1600+800+900)c{{m}^{2}}\]

\[=5050c{{m}^{2}}\]

Cuboid and Cube

A cuboid is a closed rectangular solid bounded by six rectangular faces. A cuboid has 12 edges and 8 vertices. The length, breadth and height of a cuboid is generally denoted by I, b and h respectively. A cuboid whose length, breadth and height are equal is called a cube and each equal side is called edge of the cube.

• Example:

Determine the time in which the level of the water in a rectangular tank which is 50 m long and 44 m wide will rise by 7 cm if water is flowing through a cylindrical pipe of radius 7 cm at the rate of 5 kilometre per hour.

(a) 4 hours                     (b) 3 hours

(c) 2 hours                     (d) 5 hours

(e) None of these

Answer (c)

Explanation: Let x hours be the time taken by volume of water flowing through the pipe. Then,

\[\frac{22}{7}\times {{\left( \frac{7}{100} \right)}^{2}}\times 5000\times X\]

\[=\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times 5000X\]

\[=77x{{m}^{3}}\]

Volume of tank \[=\frac{50\times 44\times 7}{100}{{m}^{3}}=154{{m}^{3}}\]

Therefore, \[77x=154\Rightarrow x=2hours\]

Cone and Cylinder

Cone is a solid form which is generated by the revolution of a right angled triangle about one of the sides adjacent to the right angle. The base of a cone is always circular. While a cylinder has two identical circular ends and one curved surface and area of each circular ends are same.

• Example:

The volume of a cylinder having a height of 14 m and base radius 3 m is:

(a)\[792\,\,{{m}^{3}}\]                         (b) \[99\,\,{{m}^{3}}\]

(c) \[198\,\,{{m}^{3}}\]                        (d) \[396\,\,{{m}^{3}}\]

(e) None of these

Answer (d)

Explanation: Volume of the cylinder \[=\pi {{r}^{2}}h\]

\[=\frac{22}{7}\times 3\times 3\times 14=396{{m}^{3}}\]

Some Important Formulae

• Lateral surface area of a cuboid \[=2h(l+b)\]
• Total surface area of a cuboid \[=2(lb+bh+hl)\]
• Volume of a cuboid \[=l\times b\times h\]
• Length of the diagonal of a cuboid = \[\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}\]
• Lateral surface area of a cube \[=4{{a}^{2}}\]
• Total surface area of a cube \[=6{{a}^{2}}\]
• Volume of a cube \[={{a}^{3}}\]
• Curved surface area of a cone \[=\pi rl\]
• Total surface area of a cone \[=\pi rl(l+r)\]
• Slant height of a cone, \[l=\sqrt{{{r}^{2}}+{{h}^{2}}}\]
• Volume of a cone \[=\frac{1}{3}\pi {{r}^{2}}h\]
• Curved surface area of a cylinder \[=2\pi rh\]
• Total surface area of a cylinder \[=2\pi r(r+h)\]

Volume of a cylinder \[=\pi {{r}^{2}}h\]