General Questions
Practice and master this topic with our carefully crafted questions.
The perimeter of one face of a cube is 20 cm. Its volume must be :
Correct Answer: A. 125 cm³ ✅
- A. 125 cm³ ✅ — Correct.
- B. 400 cm³ ❌
- C. 1000 cm³ ❌
- D. 8000 cm³ ❌
Explanation:
A face of a cube is a square.
Perimeter of one face = 20 cm.
Side of the square = 20 ÷ 4 = 5 cm.
Volume of cube = side³
= 5³
= 125 cm³.
Exam Fact:
For a cube, Volume = side³. The perimeter of one face is 4 × side.
Therefore, the correct answer is A. 125 cm³ ✅.
A rectangular water tank is 80 m × 40 m. Water flows into it though a pipe 40 Sq. cm at the opening at a speed of 10 Km/Hr. By how much, the water level will rise in the tank in half an hour ?
Correct Answer: C. 5/8 cm ✅
- A. 3/2 cm ❌
- B. 4/9 cm ❌
- C. 5/8 cm ✅ — Correct.
- D. None of these ❌
Explanation:
Dimensions of the tank = 80 m × 40 m.
Area of tank base = 80 × 40 = 3200 m².
Area of pipe opening = 40 cm² = 40/10,000 = 0.004 m².
Speed of water = 10 km/hr = 10,000 m/hr.
Volume of water flowing in 1 hour:
= 0.004 × 10,000 = 40 m³.
In half an hour:
Volume = 40 × 1/2 = 20 m³.
Let the rise in water level be h metres.
Volume = Area of tank × height
20 = 3200 × h
h = 20/3200 = 0.00625 m.
Converting to centimetres:
0.00625 × 100 = 0.625 cm = 5/8 cm.
Exam Fact:
For water tanks, use Volume = Base Area × Rise in Water Level. Also remember to convert all units to the same system before calculating.
Therefore, the correct answer is C. 5/8 cm ✅.
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 lavel in the tank will be:
Correct Answer: B. 25 cm ✅
- A. 20 cm ❌
- B. 25 cm ✅ — Correct.
- C. 35 cm ❌
- D. 50 cm ❌
Explanation:
Number of men = 50.
Displacement by each man = 4 m³.
Total volume of displaced water = 50 × 4 = 200 m³.
Base area of the tank = 40 × 20 = 800 m².
Let the rise in water level be h metres.
Volume displaced = Base area × Rise
200 = 800 × h
h = 200/800 = 0.25 m.
Converting into centimetres:
0.25 × 100 = 25 cm.
Exam Fact:
Rise in water level = Volume displaced ÷ Base area of tank.
Therefore, the correct answer is B. 25 cm ✅.
If a metallic cuboid weighs 16 Kg, how much would a miniature cuboid of metal weigh, if all dimensions are reduced to one-fourth of the original ?
Correct Answer: A. 0.25 Kg ✅
- A. 0.25 Kg ✅ — Correct.
- B. 0.50 Kg ❌
- C. 0.75 Kg ❌
- D. 1 Kg ❌
Explanation:
Original weight of the cuboid = 16 Kg.
Each dimension is reduced to 1/4 of the original.
Volume ratio = (1/4)³ = 1/64.
Since the material remains the same, weight is proportional to volume.
Weight of miniature cuboid = 16 × 1/64
= 0.25 Kg.
Exam Fact:
When all three dimensions of a solid are multiplied by a factor \(k\), its volume and weight are multiplied by k³, assuming the same material and density.
Therefore, the correct answer is A. 0.25 Kg ✅.
The capacity of a tank of dimensions (8 m × 6 m × 2.5 m) is :
Correct Answer: D. 120000 litres ✅
- A. 120 litres ❌
- B. 1200 litres ❌
- C. 12000 litres ❌
- D. 120000 litres ✅ — Correct.
Explanation:
Length = 8 m.
Breadth = 6 m.
Height = 2.5 m.
Volume of the tank = Length × Breadth × Height
= 8 × 6 × 2.5
= 120 m³.
Since 1 m³ = 1000 litres:
Capacity = 120 × 1000
= 120000 litres.
Exam Fact:
Capacity of a rectangular tank = Length × Breadth × Height. Remember that 1 m³ = 1000 litres.
Therefore, the correct answer is D. 120000 litres ✅.
A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side.Its volume is :
Correct Answer: B. 270 m³ ✅
- A. 208 m³ ❌
- B. 270 m³ ✅ — Correct.
- C. 360 m³ ❌
- D. 408 m³ ❌
Explanation:
Width of the pool = 9 m.
Length of the pool = 12 m.
Shallow-side depth = 1 m.
Deeper-side depth = 4 m.
Average depth = (1 + 4) ÷ 2 = 2.5 m.
Volume of the pool = Length × Width × Average depth
= 12 × 9 × 2.5
= 270 m³.
Exam Fact:
For a pool with a uniformly sloping bottom, Volume = Length × Width × Average depth.
Therefore, the correct answer is B. 270 m³ ✅.
The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm² . The volume of the cuboid is :
Correct Answer: B. 48 cm³ ✅
- A. 24 cm³ ❌
- B. 48 cm³ ✅ — Correct.
- C. 64 cm³ ❌
- D. 120 cm³ ❌
Explanation:
Let the edges of the cuboid be x, 2x, 3x.
Surface area = 2(lb + bh + hl) = 88 cm².
Substituting the dimensions:
2(x × 2x + 2x × 3x + 3x × x) = 88
2(2x² + 6x² + 3x²) = 88
22x² = 88
x² = 4
x = 2 cm.
Therefore, the edges are 2 cm, 4 cm and 6 cm.
Volume = l × b × h
= 2 × 4 × 6
= 48 cm³.
Exam Fact:
Surface area of a cuboid = 2(lb + bh + hl) and volume = l × b × h.
Therefore, the correct answer is B. 48 cm³ ✅.
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 get on it. The mass of man is :
Correct Answer: B. 60 kg ✅
- A. 12 kg ❌
- B. 60 kg ✅ — Correct.
- C. 72 kg ❌
- D. 96 kg ❌
Explanation:
Length of the boat = 3 m.
Breadth of the boat = 2 m.
Additional sinking = 1 cm = 0.01 m.
Volume of water displaced = Base area × Sinking depth
= 3 × 2 × 0.01
= 0.06 m³.
Since 1 m³ of water has a mass of approximately 1000 kg:
Mass of displaced water = 0.06 × 1000
= 60 kg.
The man's mass equals the mass of the additional water displaced.
Exam Fact:
For a floating object, the added load equals the weight of the additional water displaced (Archimedes' principle).
Therefore, the correct answer is B. 60 kg ✅.
The cost of the paint is Rs. 36.50 per kg. If 1kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side ?
Correct Answer: C. Rs. 876 ✅
- A. Rs. 692 ❌
- B. Rs. 768 ❌
- C. Rs. 876 ✅ — Correct.
- D. Rs. 972 ❌
- E. None of these ❌
Explanation:
Side of the cube = 8 feet.
Total outside surface area = 6 × side²
= 6 × 8 × 8
= 384 square feet.
1 kg of paint covers 16 square feet.
Paint required = 384 ÷ 16 = 24 kg.
Cost per kg = Rs. 36.50.
Total cost = 24 × 36.50 = Rs. 876.
Exam Fact:
Total surface area of a cube = 6a². Total painting cost = Paint required × Cost per kg.
Therefore, the correct answer is C. Rs. 876 ✅.
The heigth of a wall is six time its width and the length of the wall is seven times its heigth. If volume of the wall be 16128 cu. m, its width is :
Correct Answer: A. 4 m ✅
- A. 4 m ✅ — Correct.
- B. 4.5 m ❌
- C. 5 m ❌
- D. 6 m ❌
Explanation:
Let the width of the wall be x m.
Height = 6 × width = 6x m.
Length = 7 × height = 42x m.
Volume of a cuboid = Length × Breadth × Height.
Given volume = 16128 m³:
42x × x × 6x = 16128
252x³ = 16128
x³ = 16128 ÷ 252 = 64
x = ∛64 = 4 m.
Exam Fact:
Volume of a cuboid = Length × Breadth × Height. When dimensions are expressed as multiples of one variable, substitute them into the volume formula.
Therefore, the correct answer is A. 4 m ✅.