Area problems
- 1. Find the area of the square whose side is equal to the diagonal of a rectangle of length 3 cm and breadth 4 cm.
Options- A. 25 sq.cm
- B. 16 sq.cm
- C. 9 sq.cm
- D. 4 sq.cm Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, IT Trainer
Correct Answer: 25 sq.cm
Explanation:
Given length of the rectangle = 3 cm
Breadth of the rectangle = 4 cm
Then, the diagonal of the rectangle
Then, it implies side of square = 5 cm
We know that Area of square = S x S = 5 x 5 = 25 sq.cm.
- 2. The breadth of a rectangular field is 75% of its length. If perimeter of the field is 1050 m, what will be th area of field ?
Options- A. 65700 sq.m
- B. 54500 sq.m
- C. 78700 sq.m
- D. 67500 sq.m Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 67500 sq.m
Explanation:
Let the length be 'l' and breadth be 'b'.
b = l × 3/4__________(a)
2(l+b) = 1050
l+b = 525___________(b)
From equations (a) and (b),
l = 300m, b = 225 m
Area = l × b
= 300 × 225
= 67500 sq.m.
- 3. The length, breadth and height of a room are in the ratio 7:3:1. If the breadth and height are doubled while the length is halved, then by what percent the total area of the 4 walls of the room will be increased ?
Options- A. 90%
- B. 88%
- C. 85%
- D. 84% Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 90%
Explanation:
Let length, breadth and height of the room be 7, 3, 1 unit respectively.
Area of walls = 2(l+b)xh = 2(7+3)x1 = 20 sq. unit.
Now, length, breadth and height of room will become 3.5, 6 and 2 respectively.
Area of walls = 2(l+b)xh = 2(3.5+6)x2 = 38 sq. unit.
% Increase in the area of walls = (38-20)x100/20 = 90%.
- 4. What is the area of an obtuse angled triangle given below with two sides are 8 and 12 and the angle included between two sides is 150 deg?
Options- A. 48 sq units
- B. 24 sq units
- C. 12 sq units
- D. 6 sq units Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 24 sq units
Explanation:
We know that,
The area of a triangle with two sides given and included angle
A = 1/2 x product of sides x Sin(angle)
Here the two sides are 8 & 12
Angle = 150
Area = 1/2 x 8 x 12 x sin150
Sin(150) = sin(90+60) = cos(60) = 1/2
A = 48 x 1/2 = 24
Area of the given triangle = 24 sq units.
- 5. What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ?
Options- A. 13 m
- B. 14 m
- C. 15 m
- D. 16 m Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 13 m
Explanation:
The length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is
=> mts.
- 6. The length of a rope in meter by which a cow must be tethered in order that she may be able to graze an area of 2826 sq.m is ?
Options- A. 15 mts
- B. 30 mts
- C. 24 mts
- D. 36 mts Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 30 mts
Explanation:
The cow can graze an area of 2826 sq.m i.e it is able to cover area of circle of 2826 sq.m
Therefore,
=2826
=(2826×7/22) = 899.18 = 900
r = 30 m.
Therefore, the radius of the circle implies the length of the rope = 30 mts.
- 7. An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq. m ?
Options- A. Rs. 4082.40
- B. Rs. 1024.21
- C. Rs. 2810.6
- D. Rs. 3214 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: Rs. 4082.40
Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
- 8. The edge of three cubes of metal is 3 m, 4 m and 5 m. They are melted and formed into a single cube. Find the edge of the new cube ?
Options- A. 15 m
- B. 4 m
- C. 6 m
- D. 9 m Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 6 m
Explanation:
The edge of the new cube is = => a = 6 m.
- 9. The perimeter of a square is equal to twice the perimeter of a rectangle of length 8cm and breadth 7cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?
Options- A. 55.12 cm
- B. 22.54 cm
- C. 42.51 cm
- D. 38.57 cm Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 38.57 cm
Explanation:
We know that perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm
Given perimeter of square is twice the perimeter of rectangle = 2(30) = 60cm
Therefore, side of the square is = 1/4 x 60 = 15cm
Circumference of the required semicircle =
=
= 23.57 + 15 = 38.57cm.
- 10. If a 36 cm thread is used to wrap a book, lengthwise twice and breadth wise once, what is the size of the book ?
Options- A. 288 sq.cm
- B. 188 sq.cm
- C. 144 sq.cm
- D. 244 sq.cm Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 288 sq.cm
Explanation:
Length of the thread is 36 cms.
length wise twice breath wise once then totally thrice.
so 36/3 = 12.
so length is 12 x 2 = 24 cms
breath is 12 cms
Area of the book = length x breath = 24 x 12 = 288 sq.cm
Programming
Copyright ©CuriousTab. All rights reserved.