Mensuration -

What is the area of a tringle whose sides are 7cm and 9cm ?
18 √2

42 √6

12 √2

5 √3

12 √5

Option E
S = 7 + 8 + 9/2 = 24/2 = 12
Area of tringle = √ S(S – a) (S – b) (S – c)
= √ 12 * 5 * 4 * 3
= 12 √ 5
The perimeter of a square is 96 cm. If the radius of a circle is 3 cm less than the side of that square, then what is area of the circle ?
1280

1345

980

1045

1386

Option E
perimeter of square = 96cm
side of square = 96/4 = 24cm
radius of circle = 24 – 3 = 21 cm
area of circle = πr^2 = 22/7 * 21 *21 = 1386 cm^2
The area of a rectangular field is 252cm^2 and ratio between length and breadth is 9 :7. If cost of wire which is to be fenced is rs.2 per meter, then find cost of fencing the field ?
240

340

130

145

128

Option E
Let length and breadth are 9x and 7x respectively.
9x * 7x = 252
x = 2
length = 9 * 2 = 18
breadth = 7 * 2 = 14
perimeter of rectangular field = 2(18 + 14) = 64m
cost of fencing wire = 64 * 2 = 128
The perimeter of rectangle is 72m and ratio between the length and breadth is 11 : 7. What is the difference between the half of the length and one-seventh of the breadth of rectangle ?
9m

6m

12m

15m

17m

Option A
Let length and breadth of rectangle 11x and 7x respectively.
perimeter = 72m
2(11x + 7x) = 72
x = 2
length = 11 * 2 = 22
breadth = 7 * 2 = 14
difference = 22/2 – 14 * 1/7 = 11 – 2 = 9m
There are two circle A and B and diameter of circle A is equal to be the radius of circle B,. If radius of circle A is 14 cm, Then find the difference between the perimeter of two circle ?
48cm

42cm

154cm

88cm

28cm

Option D
Radius of circle A = 14 cm
Diameter of circle A = 14 * 2 = 28
radius of circle B = 28
perimeter of circle A = 2 * 22/7 * 14 = 88cm
perimeter of circle B = 2 * 22/7 * 28 = 176 cm
difference = 176 – 88 = 88cm
Curved surface area of a cylinder is 2640 cm^2 and its height is 20cm. Find the volume of a cylinder.
27720 cm^2

4840 cm^2

22350 cm^2

32430 cm^2

16340 cm^2

Option A
C.S.A = 2640
2πrh = 2640
2 * 22/7 * r * 20 = 2640
r = 2640 * 7 / 44 * 20 = 21
volume = πr^2h = 22/7 * 21 * 21 * 20 = 27720 cm^2
The length of the rectangle A is 4 m more than the breadth of rectangle and perimeter of rectangle A is 56m. What is the area of rectangle B whose length is equal to the length of rectangle A and breadth is 8 m ?
64 m^2

48 m^2

24 m^2

128 m^2

120 m^2

Option D
Let breadth of rectangle A = x
length = x + 4
perimeter = 56
2(x + x + 4) = 56
4x + 8 = 56
x = 12
length of rectangle A = 12 + 4 = 16
length of rectangle B = 16
breadth = 8
area = 16 * 8 = 128 m^2
A trapezium whose parallel sides are 18 cm and 14 cm long and distance between them ids 9cm. What is the area of trapezium ?
158 cm^2

240 cm^2

144 cm^2

152 cm^2

245 cm^2

Option C
Area of trapezium = 1/2 * (18 + 14) * 9 = 144 cm ^2
If the ratio of two curved surface area of two cylinder A and B are 4 : 5 and ratio of their radius is 2 : 1, then what is the ratio of their volumes ?
8 : 7

9 : 10

13 : 7

8 : 5

3 : 4

Option D
Let radius of cylinder A and B = r_1 and r_2
height cylinder A and B = h_1 and h_2
2πr_1 h_1 / 2πr_2 h_2 = 4/5
h_1 / h_2 * 2/1 = 4/5
h_1 / h_2 = 2/5
ratio of their volumes = π^2r_1 h_1 / π^2r_2 h_2
(2)^2 * 2 / (1)^2 * 5 = 8/5
If the radius of cone is increased by 50% and height is decreased by 40%, then find the percentage change in the volume ?
55% decrease

40% increase

45% decrease

48% increase

50% decrease

Option A
Let radius of cone = 100
after increased radius of cone = 100 + 50 = 150
ratio = 2 : 3
let height of cone = 100
after decreased radius of cone = 100 – 40 = 60
ratio = 5 : 3
volume = 1/3 * πr^2h = 1/3 * 22/7 * 4 * 5 = 440 / 21
volume = 1/3 * πr^2h = 1/3 * 22/7 * 3 * 3 = 198/21
decrease = 242 / 440 * 100 = 55%

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