The ratio of length and breadth of rectangular field is 3 : 2. If the perimeter of rectangular field is 40cm, then what is the area of square whose side 5cm more than the length of rectangular field ?
216
289
324
196
400
Option B Let length and breadth or rectangular field = 3x and 2x perimeter = 40 2(3x + 2x) = 40 10x = 40 x = 4 length = 3 * 4 = 12cm side of square = 12 + 5 = 17 Area of square = 17 * 17 = 289 cm^2
Length of two rectangles A and B is 14 cm and 20 cm respectively and sum of their breadth 14 cm. If ratio of perimeter of A and B is 5 : 7, then what is the difference between area of these rectangles ?
84
54
42
62
76
Option E Let breadth of rectangular A = x and breadth rectangular B = 14 – x perimeter of rectangular A = 2 (14 + x) perimeter of rectangle B = 2 (20 + 14 – x) = 2 (34 – x) 2 (14 + x)/2 (34 – x) = 5/7 340 – 10x = 196 + 14x x = 6 breadth of rectangle A = 6 cm breadth of rectangle B = 14 – 6 = 8 cm Area of rectangle A = 14 * 6 = 84 cm^2 Area of rectangle B = 20 * 8 = 160 cm^2 Difference = 160 – 84 = 76 cm^2
If the diagonal of a cube is of length ‘x’, then what is the lateral surface area of that cube ?
2x^2/3
5x/3
4x/3
4x^2/3
8x
Option D Diagonal of cube = a√3 a√3 = x a = x/√3 lateral surface area = 4a^2 = 4*(x/√3)^2 = 4x^2/3
If the total surface area of a cube is 8664 cm^2, the what is the length of its diagonal ?
46√3
34√3
38√3
24√3
19√2
Option C T.S.A = 8664 6a^2 = 8664 a^2 = 1444 a = 38 diagonal = a√3 = 38√3
If the ratio of radius of two spheres A and B is 3 : 5, then what is the ratio of their volumes ?
27 : 125
3 : 5
12 : 25
9 : 25
6 : 15
Option A Ratio of volume of A and B = 4/3Ï€(3)^3 : 4/3Ï€(5)^3 = 27 : 125
The ratio of length and breadth of rectangles is 5 : 3 and its area is 240 m^2. If the perimeter of square is 8m less than the perimeter of rectangles, then what is the area of square ?
324
196
1024
1444
1296
Option B Let length and breadth of rectangles = 5x and 3x Area = 240 15x^2 = 240 x = 4 length = 5 * 4 = 20 breadth = 3 * 4 = 12 perimeter of rectangle = 2 (20+ 12) = 64 perimeter of square = 64 – 8 = 56 side of square = 56/4 = 14 Area of square = 14 * 14 = 196
The non – parallel sides of a trapezium are equal to side of perimeter of square 40cm and the parallel sides are 8cm and 20cm respectively, find the perimeter of trapezium ?
38
24
20
36
40
Option D perimeter of square = 40 side of square = 40/4 = 10cm non-parallel side of trapezium = 10 one parallel side = 8cm other parallel side = 20cm breadth of tringle = 20 – 8/2 = 6 let height of trapezium = h 10^2 = h^2 + 6^2 h^2 = 64 h = 8 perimeter = 10 + 10 + 8 + 8 = 36 cm
The circumference of a circle A is equal to the perimeter of a square whose area is 1936 m^2. Diameter of circle B is four times the radius of circle A what is the area of circle B ?
4532
3952
2840
4900
9856
Option E Area of square = 1936 m^2 side of square = √1936 = 44m perimeter of square = 44 * 4 = 176m 2πr = 176 r = 176 *7 /44 = 28 diameter of circle B = 28 * 4 = 112 radius = 112/2 = 56m Area = πr^2 = 22/7 * 56 * 56 = 9856
If the height and radius of a cylinder increased by 25% and 20% respectively. Then what is the change in percent in its curved surface area ?
20%
50%
40%
25%
58%
Option B Let the height of cylinder = 4h increased height = 4h* 125/100 = 5h and radius of cylinder = 5r increased radius = 5r * 120/100 = 6r initial curved surface area = 2 * Ï€ * 4h * 5r = 40Ï€hr new curved surface area = 2 * Ï€ * 5h * 6r = 60Ï€hr % change = 60Ï€hr – 40Ï€hr/40Ï€hr * 100 = 50%
The length , breadth and height of a cuboid is 14m, 15m, 20m respectively,. Find the lateral surface area of cuboid ?
1225
1160
4250
2420
3840
Option B L.S.A = 2 * 20 (14 + 15) = 40 * 29 = 1160 m
