Area problems
- 1. In a triangle ABC, BC = 5 cm AC = 12 cm and AB = 13 cm. The length of a altitude drawn from B on AC is?
Options- A. 4 cm
- B. 5 cm
- C. 6 cm
- D. 7 cm Discuss
Correct Answer: 5 cm
Explanation:
? s= (13 + 5 + 12) / 2 cm
= 15cm
s-a = 2 cm,
s-b = 10 cm and
s-c = 3 cm
? Area = ? (15 x 2 x 10 x 3 ) cm2
= 30 cm2
? (12 x h) / 2 = 30
? h = 5 cm
- 2. The perimeter of an isosceles triangle is equal to 14 cm . The lateral side is to the base in the ratio 5 : 4 the area of the triangle is?
Options- A. 1/2?21 cm2
- B. 3/2?21 cm2
- C. ?212
- D. 2?21 cm2 Discuss
Correct Answer: 2?21 cm2
Explanation:
Let lateral side = (5y) cm and base = (4y) cm
? perimeter = 5y + 5y + 4y = 14
?y = 1
So, the sides are 5 cm , 5 cm and 4 cm
Now s= 1/2 (5 + 5 + 4) cm = 7 cm
(s-a) = 2 cm
(s-b) = 2 cm and
(s-c) = 3 cm
? Required Area = ? (7 x 2 x 2 x 3) cm2
=2?21 cm2
- 3. The sides of a triangular board are 13 meters, 14 meters and 15 meters. The cost of paining it at the rate of Rs. 8.75 per m 2 is?
Options- A. Rs. 688.80
- B. Rs. 735
- C. Rs. 730.80
- D. Rs. 722.50 Discuss
Correct Answer: Rs. 735
Explanation:
s = (13 + 14 + 15 ) / 2 = 21,
s-a = 8 ,
s-b = 7,
s-c= 6
? Area to be painted = ? [s(s-a) (s-b) (s-c)]
=? [21 x 8 x 7 x 6] m2
= 84 m2
? Cost of painting = Rs. (84 x 8.75) = Rs. 735
- 4. If the diagonal of a square is double, how does the area of the square change?
Options- A. Becomes four fold
- B. Becomes three fold
- C. Becomes two fold
- D. None of the above Discuss
Correct Answer: Becomes four fold
Explanation:
Ratio of the areas = area of original square / area of new square
= [ d2 / 2 ] / [ (2d)2 / 2 ] = 1/4
? New area becomes 4 fold.
- 5. A circle and a square have same area. The ratio of the side of the square and the radius of the circle is?
Options- A. ?? : 1
- B. 1 : ??
- C. 1 : ?
- D. ? : 1 Discuss
Correct Answer: 1 : ??
Explanation:
? Area of square = Area of circle
? x2 = ?r2
? x/r = ??
= ? ? : 1
- 6. The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is?
Options- A. 29.46 km/hr.
- B. 31.68 km/hr.
- C. 36.25 km/hr.
- D. 32.72 km/hr. Discuss
Correct Answer: 31.68 km/hr.
Explanation:
Circumference = 2?r
= 2 x (22 / 7) x 70 cm
= 440 cm
Distance travelled in 10 revolutions = 440 x 10 cm
= 4400 cm
= 44 m
? Speed = distance / time
= 44 / 5 m/sec
= (44 / 5) x (18 / 5) km/hr
= 31.68 km/hr
- 7. A circular disc of area 0.49 ? square meters, rolls down a length of 1.76 km. The number of revolutions it makes is?
Options- A. 300
- B. 400
- C. 600
- D. 4000 Discuss
Correct Answer: 400
Explanation:
Area = ?r2 = 0.49?
? r = 0.7 m
Number of revolutions = total distance / circumference
= (1.76 x 1000) / (2 x 22/7 x 0.7)
= 400
- 8. The Number of rounds that a wheel of diameter 7/11 m will make in going 4 km, is?
Options- A. 1000
- B. 1500
- C. 1700
- D. 2000 Discuss
Correct Answer: 2000
Explanation:
Number of round = total distance / circumference of wheel.
= (4 x 1000) / ?d
= (4 x 1000) / ( 22/7 x 7/11)
= 2000
- 9. A wheel makes 1000 revolutions in covering a distance of 88 km. the diameter of the wheel is?
Options- A. 24 meters
- B. 40 meters
- C. 28 meters
- D. 14 meters Discuss
Correct Answer: 28 meters
Explanation:
Distance covered in one revolution = total distance travelled / total number of revolution.
= ( 88 x 1000) / 1000 m
= 88 m
We know that the distance covered in one revolution = circumference of the wheel.
? ?d = 88
? 22d / 7 = 88
? d = 28 m
- 10. The diameter of a wheel is 63 cms. Distance travelled by the wheel in 100 revolutions is?
Options- A. 99 meters
- B. 198 meters
- C. 63 meters
- D. 136 meters Discuss
Correct Answer: 198 meters
Explanation:
Distance travelled in 1 revolution = circumference of the wheel
= ?d
= ( 22/7 ) x 63
= 198 cm
So the distance travelled in 100 revolutions = 100 x distance travelled in 1 revolution
= 100 x 198 cm
= 19800 cm
= 198 m
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