Area problems
- 1. The diameter of a circle is 105 cm less than the circumference. What is the diameter of the circle?
Options- A. 44 cm
- B. 46 cm
- C. 48 cm
- D. 49 cm Discuss
Correct Answer: 49 cm
Explanation:
? ?d-d = 105 cm
? (? -1 ) d = 105 cm
? [(22/7)-1] x d = 105 cm
? d = (7/15) x 105 cm = 49 cm
- 2. The area of the sector of a circle, whose radius is 12 meters and whose angle at the centre is 42, is?
Options- A. 26.4 sq. meters
- B. 39.6 sq. meters
- C. 52.8 sq. meters
- D. 79.2 sq. meters Discuss
Correct Answer: 52.8 sq. meters
Explanation:
Area of the sector = [(22/7) x 12 x 12] x [42°/360°] m2
= 52.8 m2
- 3. In a circle of radius 21 cm an arc subtends an angle of 72° at the centre. The length of the arc is?
Options- A. 13.2 cm
- B. 19.8 cm
- C. 21.6 cm
- D. 26.4 cm Discuss
Correct Answer: 26.4 cm
Explanation:
Arc length = 2?r (?° / 360°)
= 2 x (22/7) x 21 x (72° / 360°) cm
= 26.4 cm
- 4. The area of sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm is?
Options- A. 35 sq.cms
- B. 17.5 sq.cms
- C. 8. 75 sq.cms
- D. 55 sq.cms Discuss
Correct Answer: 8. 75 sq.cms
Explanation:
Area of sector = ( arc length x radius ) / 2 cm2
= (3.5 x 5 ) / 2
= 8.75 cm2
- 5. A rectangular carpet has an area of 120 sq. m and a perimeter of 46 m . The length of its diagonal is?
Options- A. 15 m
- B. 16 m
- C. 17 m
- D. 20 m Discuss
Correct Answer: 17 m
Explanation:
Let length = a metres and breadth = b metres
Then, 2(a+b)= 46
? (a+b) =23 and ab =120
? Diagonal = ?a2 + b2
?(23)2-2 x 120
?289 = 17 m
- 6. Radhika runs along the boundary of a rectangular park at the rate of 12 km/hr and completes one full round in 15 minutes. If the length of the park is 4 times its breadth , the area of the park is?
Options- A. 360000 m2
- B. 360002
- C. 3600 m2
- D. None of these Discuss
Correct Answer: 360000 m2
Explanation:
Speed = 12 x (5/18) m/sec
=10/3 m/sec
there4; perimeter = (10/3) x 15 x 60 m=3000 m
? 2( a + 4a) = 3000 m
? a = 300 m
So, length = 1200 m and breadth = 300 m
? Area = (1200 x 300 ) m2 = 360000m2
- 7. If D,E and F are respectively the midpoint of the sides BC , CA and AB of a ? ABC and the area of ? ABC = 36m 2. Then area of ? DEF is?
Options- A. 12 cm 2
- B. 9 cm 2
- C. 18 cm2
- D. 19 cm2 Discuss
Correct Answer: 9 cm 2
Explanation:
Area of a triangle formed by joining the mid point of the sides of the triangle is 1/4th of area of the original triangle .
So area of ? DEF = 36/ 4 = 9 m2
- 8. A rectangular carpet has an area of 60 sq. m. Its diagonal and longer side together equal 5 times the shorter side, The length of the carpet is?
Options- A. 5 m
- B. 12 m
- C. 13 m
- D. 14.5 m Discuss
Correct Answer: 12 m
Explanation:
Let the longer side = l, shorter side = b and diagonal = d
Then, area of rectangular carpet = l x b = 60 ....(1)
And from question d + l = 5b
? d = 5b - l ...(2)
? d2 = 25b2 + l2 - 10 x lb
? l2+ b2 = 25b2 + l2 - 10 x lb
? l2+b2 = 25b2 + l2 - 10 x 60
? 24b2 = 600
? b = ?25 = 5 m
? l = 60 / b = 60 / 5 = 12 m
- 9. In ? ABC ,sides BC = 10 cm and height AD = 4.4 cm. If AC = 11 cm. Then altitude BE equals?
Options- A. 5 cm
- B. 4 cm
- C. 5.6 cm
- D. 5.5 cm Discuss
Correct Answer: 4 cm
Explanation:
We know that area of triangle = ( base x height ) / 2
So area of triangle = (BC x AD) / 2 = (AC x BE) / 2
? (10 x 4.4) / 2 = (11 x h) / 2
? h= (10 x 4.4)/11 = 4 cm
- 10. The cross section of a canal is a trapezium in shape . If the canal is a trapezium in shape. If the canal is 10 meters wide at the top and 6 meters wide at bottom and the area of cross section is 640 sq. meters The depth of canal is?
Options- A. 40 meters
- B. 80 meters
- C. 160 meters
- D. 384 meters Discuss
Correct Answer: 80 meters
Explanation:
Cross section area = 1/2 x ( a + b ) x d
where a and b are the parallel sides, d is the perpendicular distance between them.
? 1/2 x ( a + b ) x d = 640
? d = (640 x 2) / 16 = 80m
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