Discussion
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- Question
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
Options- A. 12 kg
- B. 60 kg
- C. 72 kg
- D. 96 kg
- Correct Answer
- 60 kg
ExplanationVolume of water displaced = (3 x 2 x 0.01) m3 = 0.06 m3. ∴ Mass of man = Volume of water displaced x Density of water = (0.06 x 1000) kg = 60 kg. - 1. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options- A. 49 m2
- B. 50 m2
- C. 53.5 m2
- D. 55 m2 Discuss
- 2. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
Options- A. 10
- B. 20
- C. 40
- D. 73 Discuss
- 3. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
Options- A. 35 years
- B. 40 years
- C. 50 years
- D. None of these Discuss
- 4. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options- A. 76 kg
- B. 76.5 kg
- C. 85 kg
- D. Data inadequate
- E. None of these Discuss
- 5. A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
Options- A. 250
- B. 276
- C. 280
- D. 285 Discuss
- 6. How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
Options- A. 5600
- B. 6000
- C. 6400
- D. 7200 Discuss
- 7. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
Options- A. 12Π cm3
- B. 15Π cm3
- C. 16Π cm3
- D. 20Π cm3 Discuss
- 8. The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
Options- A. 3 : 7
- B. 7 : 3
- C. 6 : 7
- D. 7 : 6 Discuss
- 9. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
Options- A. 344.35 cm2
- B. 462 cm2
- C. 498.35 cm2
- D. None of these Discuss
- 10. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
Options- A. 20 cm
- B. 25 cm
- C. 35 cm
- D. 50 cm Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 49 m2
Explanation:
| Area of the wet surface | = [2(lb + bh + lh) - lb] |
| = 2(bh + lh) + lb | |
| = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2 | |
| = 49 m2. |
Correct Answer: 40
Explanation:
Let there be x pupils in the class.
| Total increase in marks = | ❨ | x x | 1 | ❩ | = | x |
| 2 | 2 |
| ∴ | x | = (83 - 63) ⟹ | x | = 20 ⟹ x= 40. |
| 2 | 2 |
Correct Answer: 40 years
Explanation:
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.
∴ Husband's present age = (90 - 50) years = 40 years.
Correct Answer: 85 kg
Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Correct Answer: 285
Explanation:
Since the month begins with a Sunday, to there will be five Sundays in the month.
| Required average |
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| = 285 |
Correct Answer: 6400
Explanation:
| Number of bricks = | Volume of the wall | = | ❨ | 800 x 600 x 22.5 | ❩ | = 6400. |
| Volume of 1 brick | 25 x 11.25 x 6 |
Correct Answer: 12Π cm3
Explanation:
Clearly, we have r = 3 cm and h = 4 cm.
| ∴ Volume = | 1 | Πr2h = | ❨ | 1 | x Π x 32 x 4 | ❩cm3 | = 12Π cm3. |
| 3 | 3 |
Correct Answer: 7 : 3
Explanation:
| Πr2h | = | 924 | ⟹ r = | ❨ | 924 | x 2 | ❩ | = 7 m. |
| 2Πrh | 264 | 264 |
| And, 2Πrh = 264 ⟹ h = | ❨ | 264 x | 7 | x | 1 | x | 1 | ❩ | = 6m. |
| 22 | 2 | 7 |
| ∴ Required ratio = | 2r | = | 14 | = 7 : 3. |
| h | 6 |
Correct Answer: 498.35 cm2
Explanation:
h = 14 cm, r = 7 cm.
So, l = √(7)2 + (14)2 = √245 = 7√5 cm.
| ∴ Total surface area | = Πrl + Πr2 | |||||||||
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| = [154(√5 + 1)] cm2 | ||||||||||
| = (154 x 3.236) cm2 | ||||||||||
| = 498.35 cm2. |
Correct Answer: 25 cm
Explanation:
Total volume of water displaced = (4 x 50) m 3 = 200 m 3 .
| ∴ Rise in water level = | ❨ | 200 | ❩m 0.25 m = 25 cm. |
| 40 x 20 |
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