Q.1 Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get for their crops?
Solution : Let ABCD be the field.
Perimeter = 400 m
So, each side = 400 m ??4 = 100 m.
i.e. AB = AD = 100 m.
Let diagonal BD = 160 m.
Then semi-perimeter s of ??ABD is given by
100 + 100 +160 /2
m = 180 m
Therefore, area of ??ABD = 180(180 ??100) (180 – 100) (180 – 160)
= 180 ??80 ??80 ??20 m2 = 4800 m2
Therefore, each of them will get an area of 4800 m2 .
Q.2 Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden box covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively how many square sheets of paper of side 40 cm would she require?
Solution : Since Mary wants to paste the paper on the outer surface of the box; the quantity of paper
required would be equal to the surface area of the box which is of the shape of a cuboid. The dimensions
of the box are:
Length =80 cm, Breadth = 40 cm, Height = 20 cm.
The surface area of the box = 2(lb + bh + hl)
= 2[(80 × 40) + (40 × 20) + (20 × 80)] cm2
= 2[3200 + 800 + 1600] cm2
= 2 × 5600 cm2 = 11200 cm2
The area of each sheet of the paper = 40 × 40 cm2
= 1600 cm2
Therefore, number of sheets required =
surface area of box
area of one sheet of paper
So, she would require 7 sheets.
Q.3 Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the tiles is ` 360 per dozen.
Solution : Since Hameed is getting the five outer faces of the tank covered with tiles, the would need to know the surface area of the tank, to decide on the number of tiles required.
Edge of the cubical tank = 1.5 m = 150 cm (= a)
So, surface area of the tank = 5 × 150 × 150 cm2
Area of each square tile = side × side = 25 × 25 cm2
So, the number of tiles required =
surface area of the tank
area of each tile
Cost of 1 dozen tiles, i.e., cost of 12 tiles = ` 360
Therefore, cost of one tile = `
= ` 30
So, the cost of 180 tiles = 180 × ` 30 = ` 5400
Q.4 Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. (see Fig 13.10). What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius?
Solution : Radius of the base of the cylindrical kaleidoscope (r) = 3.5 cm.
Height (length) of kaleidoscope (h) = 25 cm.
Area of chart paper required = curved surface area of the kaleidoscope
= 2 * 22/7 * 3.5 * 25
= 550 cm2
Q.5 A corn cob , shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length (height) as 20 cm. If each 1 cm2 of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob.
Solution : Since the grains of corn are found only on the curved surface of the corn cob, we would need to know the curved surface area of the corn cob to find the total number of grains on it. In this question, we are given the height of the cone, so we need to find its slant height.
Here, l = r 2 ??h2 = (2.1)2 ??202 cm
= 404.41 cm = 20.11 cm
Therefore, the curved surface area of the corn cob = ?rl
= 22/7 × 2.1 × 20.11 cm2 = 132.726 cm2 = 132.73 cm2 (approx.)
Number of grains of corn on 1 cm2 of the surface of the corn cob = 4
Therefore, number of grains on the entire curved surface of the cob
= 132.73 × 4 = 530.92 = 531 (approx.)
So, there would be approximately 531 grains of corn on the cob.