General Questions
Practice and master this topic with our carefully crafted questions.
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is :
Correct Answer: B. 1 dm ✅
- A. 90 cm ❌
- B. 1 dm ✅ — Correct.
- C. 1 m ❌
- D. 1.1 m ❌
Explanation:
Capacity of the cistern = 8000 litres = 8 m³.
External length = 3.3 m, external breadth = 2.6 m.
Wall thickness = 5 cm = 0.05 m.
Internal length = 3.3 − 2(0.05) = 3.2 m.
Internal breadth = 2.6 − 2(0.05) = 2.5 m.
Let the internal height be h.
3.2 × 2.5 × h = 8
8h = 8
h = 1 m.
External height = 1.1 m.
Thickness of bottom = 1.1 − 1 = 0.1 m = 10 cm = 1 dm.
Exam Fact:
For a cistern, capacity = internal length × internal breadth × internal height. Remember that 1 dm = 10 cm.
Therefore, the correct answer is B. 1 dm ✅.
How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, will be needed to build a wall 8 m × 6 m × 22.5 cm ?
Correct Answer: C. 6400 ✅
- A. 5600 ❌
- B. 6000 ❌
- C. 6400 ✅ — Correct.
- D. 7200 ❌
Explanation:
Dimensions of the wall = 8 m × 6 m × 22.5 cm.
Convert metres into centimetres:
8 m = 800 cm and 6 m = 600 cm.
Volume of the wall = 800 × 600 × 22.5
= 10,800,000 cm³.
Volume of one brick = 25 × 11.25 × 6
= 1687.5 cm³.
Number of bricks = 10,800,000 ÷ 1687.5
= 6400 bricks.
Exam Fact:
Number of bricks = Volume of wall ÷ Volume of one brick. All dimensions must be in the same unit.
Therefore, the correct answer is C. 6400 ✅.
If the areas of the three adjacent faces of a cuboidal box are 120 cm², 72 cm² and 60 cm² respectively, then Find the volume of the box.
Correct Answer: A. 720 cm³ ✅
- A. 720 cm³ ✅ — Correct.
- B. 864 cm³ ❌
- C. 7200 cm³ ❌
- D. (72)² cm³ ❌
Explanation:
Let the dimensions of the cuboid be l, b, h.
Given adjacent face areas:
lb = 120 cm²
bh = 72 cm²
lh = 60 cm²
Multiplying the three equations:
(lb)(bh)(lh) = 120 × 72 × 60
(lbh)² = 518400
Taking the square root:
Volume = lbh = √518400
= 720 cm³.
Exam Fact:
When the three adjacent face areas of a cuboid are known, Volume = √(Area₁ × Area₂ × Area₃).
Therefore, the correct answer is A. 720 cm³ ✅.
How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge ?
Correct Answer: B. 216 ✅
- A. 36 ❌
- B. 216 ✅ — Correct.
- C. 218 ❌
- D. 432 ❌
Explanation:
Edge of the large cube = 18 cm.
Edge of each small cube = 3 cm.
Number of small cubes along each edge = 18 ÷ 3 = 6.
Total number of cubes = 6 × 6 × 6
= 6³
= 216 cubes.
Exam Fact:
Number of smaller cubes = (Large cube edge ÷ Small cube edge)³.
Therefore, the correct answer is B. 216 ✅.
The capacity of a cylindrical tank is 246.4 litres. If the heigth is 4 metres, what is the diameter of the base ?
Correct Answer: E. None of these ✅
- A. 1.4 m ❌
- B. 2.8 m ❌
- C. 14 m ❌
- D. 28 m ❌
- E. None of these ✅ — Correct.
Explanation:
Capacity = 246.4 litres.
Since 1000 litres = 1 m³:
Volume = 246.4 ÷ 1000 = 0.2464 m³.
Height = 4 m.
Volume of a cylinder = πr²h.
0.2464 = (22/7) × r² × 4
r² = 0.2464 ÷ (88/7) = 0.0196
r = √0.0196 = 0.14 m.
Diameter = 2 × radius = 2 × 0.14 = 0.28 m.
Since 0.28 m is not listed among the options, the answer is None of these.
Exam Fact:
Volume of a cylinder = πr²h. Always convert litres into cubic metres when the dimensions are in metres.
Therefore, the correct answer is E. None of these ✅.
The volumes of two cubes area in the ratio 8 : 27. The ratio of their surface areas is :
Correct Answer: B. 4 : 9 ✅
- A. 2 : 3 ❌
- B. 4 : 9 ✅ — Correct.
- C. 12 : 9 ❌
- D. None of these ❌
Explanation:
The ratio of the volumes of two cubes = 8 : 27.
Volume of a cube = side³.
Therefore, the ratio of their sides = ∛8 : ∛27
= 2 : 3.
Surface area of a cube = 6 × side².
Therefore, the ratio of their surface areas = 2² : 3²
= 4 : 9.
Exam Fact:
For cubes, the ratio of volumes is the cube of the ratio of sides, while the ratio of surface areas is the square of the ratio of sides.
Therefore, the correct answer is B. 4 : 9 ✅.
A cuboidal block of 6 cm × 9 cm × 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be :
Correct Answer: C. 24 ✅
- A. 6 ❌
- B. 9 ❌
- C. 24 ✅ — Correct.
- D. 30 ❌
Explanation:
Dimensions of the cuboid = 6 cm × 9 cm × 12 cm.
To get the least number of equal cubes, we need the largest possible cube edge, which is the HCF of 6, 9 and 12.
HCF(6, 9, 12) = 3 cm.
Number of cubes along the length = 12 ÷ 3 = 4.
Number of cubes along the breadth = 9 ÷ 3 = 3.
Number of cubes along the height = 6 ÷ 3 = 2.
Total number of cubes = 4 × 3 × 2 = 24.
Exam Fact:
To cut a cuboid into the least number of equal cubes, use the HCF of its three dimensions as the side length of each cube.
Therefore, the correct answer is C. 24 ✅.
2(15 + 12) x h = 2(15 x 12)
 h = |
180 | m = | 20 | m. |
| 27 | 3 |
 Volume = |
 |
15 x 12 x | 20 |  m3 |
= 1200 m3. |
| 3 |
A cistern 6 m long 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is :
Correct Answer: A. 49 m² ✅
- A. 49 m² ✅ — Correct.
- B. 50 m² ❌
- C. 53.5 m² ❌
- D. 55 m² ❌
Explanation:
Length of the cistern = 6 m.
Width = 4 m.
Water depth = 1 m 25 cm = 1.25 m.
The wet surface includes the bottom and the four sides in contact with water.
Bottom area = 6 × 4 = 24 m².
Area of two longer sides = 2 × (6 × 1.25) = 15 m².
Area of two shorter sides = 2 × (4 × 1.25) = 10 m².
Total wet surface area = 24 + 15 + 10 = 49 m².
Exam Fact:
Wet surface area of an open rectangular cistern = lb + 2lh + 2bh, where h is the depth of water.
Therefore, the correct answer is A. 49 m² ✅.
If the volumes of two cubes are in the ratio 27 : 1, the ratio of their edges is :
Correct Answer: C. 3 : 1 ✅
- A. 1 : 3 ❌
- B. 1 : 27 ❌
- C. 3 : 1 ✅ — Correct.
- D. 27 : 1 ❌
Explanation:
Ratio of the volumes of two cubes = 27 : 1.
Volume of a cube = side³.
Therefore, the ratio of their edges is the cube root of the volume ratio:
∛27 : ∛1
= 3 : 1.
Exam Fact:
For cubes, ratio of edges = cube root of the ratio of volumes.
Therefore, the correct answer is C. 3 : 1 ✅.