General Questions
Practice and master this topic with our carefully crafted questions.
A metallic sheet is of rectangular shape with dimensions 48 m × 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m³) is :
Correct Answer: B. 5120 m³ ✅
- A. 4830 m³ ❌
- B. 5120 m³ ✅ — Correct.
- C. 6420 m³ ❌
- D. 8960 m³ ❌
Explanation:
Length of the rectangular sheet = 48 m.
Breadth = 36 m.
Side of each square cut from the corners = 8 m.
Height of the open box = 8 m.
New length = 48 − 2(8) = 32 m.
New breadth = 36 − 2(8) = 20 m.
Volume of the box = Length × Breadth × Height
= 32 × 20 × 8
= 5120 m³.
Exam Fact:
When squares are cut from all four corners of a rectangular sheet, the box dimensions become (L − 2x) × (B − 2x) × x, where x is the side of each cut-out square.
Therefore, the correct answer is B. 5120 m³ ✅.
The cost of painting the whole surface area of a cube at the rate of 13 paise per sq. cm is Rs.343.98. Then the volume of the cube is :
Correct Answer: D. 9261 cm³ ✅
- A. 8500 cm³ ❌
- B. 9000 cm³ ❌
- C. 9250 cm³ ❌
- D. 9261 cm³ ✅ — Correct.
Explanation:
Cost of painting = Rs. 343.98.
Painting rate = 13 paise per cm² = Rs. 0.13 per cm².
Total surface area of the cube = Total cost ÷ Rate
= 343.98 ÷ 0.13
= 2646 cm².
Surface area of a cube = 6a².
6a² = 2646
a² = 2646 ÷ 6 = 441
a = √441 = 21 cm.
Volume of the cube = a³
= 21 × 21 × 21
= 9261 cm³.
Exam Fact:
Total surface area of a cube = 6a², and its volume = a³.
Therefore, the correct answer is D. 9261 cm³ ✅.
External radius = 4 cm,
Internal radius = 3 cm.
| Volume of iron |
|
||||||
|
|||||||
| = 462 cm3. |
Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.
Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3.
| Volume 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. |
Let the length of the wire be h.
| Radius = | 1 | mm | = | 1 | cm. | Then, |
| 2 | 20 |
 |
22 | x | 1 | x | 1 | x h = 66. |
| 7 | 20 | 20 |
| h = |
 |
66 x 20 x 20 x 7 |  |
= 8400 cm = 84 m. |
| 22 |
1 hectare = 10,000 m2
So, Area = (1.5 x 10000) m2 = 15000 m2.
| Depth = | 5 | m | = | 1 | m. |
| 100 | 20 |
| Volume = (Area x Depth) = |
|
15000 x | 1 | m3 |
|
| 20 |
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. |
Total volume of water displaced = (4 x 50) m3 = 200 m3.
| Rise in water level = |
|
200 | m 0.25 m |
| 40 x 20 |
m2 m2 m2 m2l = 10 m,
h = 8 m.
So, r = l2 - h2 = (10)2 - 82 = 6 m.
Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.