1. The ratio between the length of the rectangle and breadth of the rectangle is 7 : 4. If the perimeter of the rectangle is 198 cm and the side of the square is 10 cm less than the breadth of the rectangle, then find the area of the square?
A) 676 B) 1225 C) 144 D) 625 E) 1089
Explanation:
Perimeter of the rectangle = 2(l + b)
198 = 2(7x + 4x)
198 = 22x
x = 9 Length of rectangle = 7x = 7 × 9 = 63
Breadth of rectangle = 4x = 4 × 9 = 36
∴ Side of square (a) = 36 − 10 = 26
area of the square = a2 = (26)2 = 676
Ans: A
2. The respective ratio of radii of two right circular cylinders (A and B) is 2 : 5. The respective ratio of the heights of cylinders A and B is 3 : 1. What is the respective ratio of volumes of cylinders A and B?
A) 3 : 5 B) 12 : 35 C) 9 : 25 D) 12 : 25 E) 9 : 20
Explanation:
A : B radii → 2 : 5
height → 3 : 1
volume → πr 1 2h : πr2 2h
π × 22 × 3 : π × 52 × 1
π × 12 : π × 25
12 : 25
Ans: D
3. The length of a rectangle is 3 m more than the side of a square and the breadth of the rectangle is 3 m less than the side of the same square. If the area of the square is 196 sq.m, what is the area of the rectangle? (In sq.m)
A) 181 B) 179 C) 187 D) 183 E) 175
Explanation: Area of the square (a2) = 196
Side of square (a) = 14
Length of rectangle = 14 + 3 = 17
Breadth of rectangle = 14 − 3 = 11
Area of the rectangle = l × b = 17 × 11 = 187 sq.m
Ans: C
4. The radius of a circular field is equal to the side of a square field. If the difference between the area of the circular field and that of the square field is 105 m, what is the perimeter of the circular field? (In meters)
A) 132 B) 176 C) 88 D) 112 E) 44
Explanation: Radius of circle (r) = side of square (a)
Ans: E
5. A rectangular plot, 33 m long and 29 m broad, has two concrete crossroads running in the middle of it. One parallel to the length and the other parallel to the breadth. The rest of the plot is used as a lawn. If the width of each of the crossroads is 6m, what is the area of the lawn? (In m2)
A) 621 B) 606 C) 637 D) 642 E) 618
Explanation
Area of cross roads = w(l + b − w) = 6(33 + 29 − 6) = 336
Area of plot = 33 × 29 = 957
∴ Then area of lawn = 957 − 336 = 621
Ans: A
6. The area of a rectangle is equal to the area of a square whose diagonal is 12√ 6 m. If the difference between length and breadth of the rectangle is 6 m, what is the perimeter of the rectangle? (In m)
A) 96 B) 76 C) 72 D) 84 E) 88
Explanation: Diagonal of square = a√ 2
Area of square (a2) = (12√ 3)2 = 432
Area of rectangle = area of square
Area of rectangle (l × b) = 432 l − b = 6
∴ l = 24, b = 18
Perimeter of rectangle = 2(l + b) = 2(24 + 18) = 84 m
Ans: D
7. A rectangular plot, 41 m long and 33 m broad, has two concrete crossroads (of equal width) running in the middle of it - One parallel to the length and the other parallel to the breadth. The rest of the plot is used as a lawn. If the area of the lawn is 1073 m2, what is the width of each of the crossroads? (In m)
A) 2.5 B) 5 C) 4.5 D) 4 E) 3
Explanation:
Area of rectangle = 41 × 33 = 1353
Area of the lawns = 1073
Area of crossroads = 1353 − 1073 = 280
280 = (41 + 33 − w) w 280 = (74 − w)w
w = 4
Ans: D
8.The perimeter of an equilateral triangle is 54cm. If the side of the triangle is 3cm less than the radius of a circle, what is the difference between the circumference of the circle and perimeter of the triangle? (In m)
A) 81 B) 86 C) 78 D) 68 E) 74
Explanation: Perimeter of equilateral triangle = 3a
3a = 54 Side of triangle (a) = 18
Radius of circle = 18 + 3 = 21
Circumference of circle
= 132
Required difference = 132 − 54 = 78
Ans: C
9. The volume of a cylinder is 5775 m3 the curved surface area of the same cylinder is 660 m2. What is the total surface area of the cylinder (in m2)?
A) 2565 B) 2585 C) 2615 D) 2345 E) 2725
Explanation: Volume of cylinder = πr2h = 5775 Curved surface area of cylinder (2πrh) = 660
Ans: B
10. A cylindrical jar whose base has a radius of 18 cm is filled with water up to a height of 35 cm. A solid iron spherical ball of radius 15 cm is dropped in the jar to submerge completely in water. Find the increase in the level of water (in cm)
A) 14 B) 19 C) 20 D) 22 E) 18
Volume of water jar = volume of sphere
Ans: A
11. The perimeter of rectangle is equal to the twice the diameter of circle whose area is 616 cm2, find the area of rectangle if the length of the rectangle is 150% more than the breadth of the rectangle.
A) 160 B) 200 C) 140 D) 180 E) 100
Explanation: Area of the circle (πr2) = 616
r = 14
diameter of circle = 28
2(l + b) = 2 × 28
l = 250% b l = 10x b = 4x
10x + 4x = 28
x = 2
l × b = (10 × 2) × (4 × 2) = 160
Ans: A
12. Half of the total surface area of a sphere is 847 cm2 less than the half of total surface area of a hemisphere. If the ratio between the radius of the hemisphere and the sphere is 3 : 2, then find the radius of hemisphere.
A) 21 B) 14 C) 10.5 D) 7 E) 17.5
Explanation: Total surface area of sphere = 4πr2 Total surface area of hemisphere = 3πr2
x = 7 Radius of hemisphere = 3x = 3 × 7 = 21
Ans: A
13. Ratio of the perimeter of the square to the perimeter of the rectangle is 8 : 7 and the ratio of the length to breadth of the rectangle is 4 : 3 and the side of the square is 5 m more than the breadth of the rectangle. Find the area of the square.
A) 441 B) 400 C) 631 D) 80 E) 625
21x + 35 = 16x + 12x
7x = 35
x = 5
a = (3x + 5) ⇒ 3 × 5 + 5 = 20 a2 = 400
Ans: B
