Area problems
- 1. Chord AB of a circle when extended meets the tangent to the circle at point P. PT is the tangent touching the circle at point T. If lengths of PT and PB are 6 cm and 4 cm respectively, what is the length of PA?
Options- A. 12 cm
- B. 11 cm
- C. 10 cm
- D. 9 cm Also asked in: AIEEE, Bank Exams, CAT
Correct Answer: 9 cm
- 2. 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.
- 3. 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
- 4. The area of a square is 1024 sq.cm. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square ?
Options- A. 14:9
- B. 13:12
- C. 16:5
- D. 17:13 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 16:5
Explanation:
Area of a square SxS = 1024 => S = 32 cm
Length of the rectangle = 32x2 cm = 64 cm
Breadth of the rectangle = 32 - 12 = 20 cm
Required ratio = 64 : 20 = 16 : 5
- 5. A rectangular grassy plot 120 m. by 60 m has a gravel path 1.5 m wide all round it on the inside. Find the cost of gravelling the path at 65 paise per sq. metre ?
Options- A. Rs. 345.15
- B. Rs. 245.1
- C. Rs. 234.18
- D. Rs. 456.65 Also asked in: CAT, Bank Exams, Bank PO
Correct Answer: Rs. 345.15
Explanation:
area of the plot = 120m x 60m = 7200 sq.m
area of plot excluding gravel = 117m x 57m = 6669 sq.m
area of gravel = 7200 sq.m - 6669 sq.m = 531 sq.m
cost of building it = 531 sq.m x 65 ps = 34515 ps
In Rs. = 34515/100 = Rs. 345.15.
- 6. The perimeter of an isosceles triangle is 32 cm and each of the equal sides is 5/6 times of the base. What is the area (in cm2 ) of the triangle ?
Options- A. 39
- B. 48
- C. 57
- D. 64 Also asked in: AIEEE, Bank Exams, CAT
Correct Answer: 48
- 7. If 4 circles of equal radius are drawn with vertices of a square as the centre , the side of the square being 7 cm, find the area of the circles outside the square ?
Options- A. 119.21 sq cm
- B. 115.395 sq cm
- C. 104.214 sq cm
- D. 111.241 sq cm Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 115.395 sq cm
Explanation:
Because each vertice of the square is the center of a circle
(1/4) part of the total area of each circle inside of the square.
(3/4) part of the total area of each circle outside of the square.
Thus total area outside the square is
= 115.3955 sq cm.
- 8. A rectangular lawn of dimensions 80 m x 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m ?
Options- A. Rs. 3600
- B. Rs. 3800
- C. Rs. 3900
- D. Rs. 3700 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: Rs. 3900
Explanation:
Area = (l + b ? d) d
= (80 + 60 ? 10)10
=> 1300 sq.mts
=> 1300 x 3 = Rs.3900
- 9. The length and breadth of a rectangle is in the ratio of 3 : 1. If its perimeter is 96 m, then what is the length of the rectangle?
Options- A. 36m
- B. 24m
- C. 12m
- D. 48m Also asked in: AIEEE, Bank Exams, CAT
Correct Answer: 36m
Explanation:
Let the length of the rectangle be 3x and breadth be 1x
Given, perimeter = 96 m
2(l + b) = 96 (or) l + b = 48 (or) 3x + 1x = 48 (or) x = 12 m
Now, Length of the rectangle = 12 x 3 = 36 m
- 10. Find the length of the altitude of an equilateral triangle of side 33 cm.
Options- A. 4.5
- B. 3.5
- C. 2.5
- D. 6.5 Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 4.5
Explanation:
Let the length of the altitude be h.
Then, h =
=
= 4.5
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