The length of a hall is 20 m and width 16 m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.

Let the height of the hall be h m.
Area of the floor = l x b
= 20 x 16 = 320 m2 Area of the flat roof = l x b
= 20 x 16 = 320 m2 Sum of the areas of the four walls = 2(l + b) h
= 2(20 + 16) h = 72 h m2 According to the question,
72 h = 320 + 320

rightwards double arrow space space space space space 72 straight h space equals space 640 space space space space rightwards double arrow space straight h equals 640 over 72
rightwards double arrow space space space space space straight h space equals space 80 over 9 space straight m

Hence, the height of the hall is 80 over 9 space straight m.

1379 Views

Find the mean of each of the following distributions :

(i)

xi

10

15

20

25

30

35

40

Total

fi

4

6

8

18

6

5

3

50

(ii)

xi

12

13

14

15

16

17

18

Total

fi

1

3

4

8

10

3

1

30

(iii)

xi

50

75

100

125

150

175

200

Total

fi

12

18

50

70

25

15

10

200


(i)

xi

fi

fixi

10

4

40

15

6

90

20

8

160

25

it

450

30

6

180

35

5

175

40

3

120

Total

50

1215


Mean space equals space fraction numerator sum straight f subscript straight i straight x subscript straight i over denominator sum straight f subscript straight i straight x subscript straight i end fraction equals 1215 over 50 equals 24.3

xi

fi

fixi

12

1

12

13

3

39

14

4

56

15

8

120

16

10

160

17

3

51

18

1

18

Total

30

456


Mean equals fraction numerator sum straight f subscript straight i straight x subscript straight i over denominator sum straight f subscript straight i end fraction equals 456 over 30 equals 15.2

(iii)

xi

fi

fixi

50

12

600

75

18

1350

100

50

5000

125

70

8750

150

25

3750

175

15

2625

200

10

2000

Total

200

24075


Mean equals fraction numerator sum straight f subscript straight i straight x subscript straight i over denominator sum straight f subscript straight i end fraction equals 24075 over 200 equals 120.375
84 Views

If the edges of a cuboid are l, b and h respectively, then the total surface area of the cuboid is
  • 2(lb + bh + hl)

  • Ibh
  • 2(l + b)h
  • 2(l + b)h

A.

2(lb + bh + hl)

149 Views

The lateral surface area of a cube of side a is

  • 4a2 
  • 6a2
  • 3a2
  • 3a2

A.

4a2 
87 Views

The lateral surface area of a cuboid of length l, breadth b and height h is

  • 2(lb + bh + hl) 
  • 2(l + b)h
  • Ibh 
  • Ibh 

B.

2(l + b)h
110 Views

The total surface area of a cube of side a is 
  • 4a2 
  • 6a2
  • 3a2  
  • 3a2  

B.

6a2
91 Views