1. What is the total surface area of a cube with side length 4 cm?
Answer:
Explanation:
Total surface area of a cube = 6 × (side length)² = 6 × 4² = 96 cm².
2. A cuboid has dimensions 5 cm, 3 cm, and 4 cm. What is its volume?
Answer:
Explanation:
Volume of a cuboid = length × width × height = 5 × 3 × 4 = 60 cm³.
3. The length of a cube is increased by 2 cm. If the original length was 3 cm, what is the new volume?
Answer:
Explanation:
New length = 3 cm + 2 cm = 5 cm. New volume = 5³ = 125 cm³.
4. A cuboid with dimensions 6 cm, 4 cm, and 2 cm has its length doubled. What is the new volume?
Answer:
Explanation:
New dimensions = 12 cm × 4 cm × 2 cm. New volume = 12 × 4 × 2 = 96 cm³.
5. What is the total surface area of a cuboid with dimensions 10 cm, 7 cm, and 5 cm?
Answer:
Explanation:
Total surface area = 2(lw + lh + wh) = 2(10×7 + 10×5 + 7×5) = 290 cm².
6. If each side of a cube is halved, what happens to its volume?
Answer:
Explanation:
New volume = (1/2 side)³ = (1/2)³ original volume = 1/8 original volume.
7. A cube has a volume of 343 cm³. What is the length of each side?
Answer:
Explanation:
Side length = cube root of volume = ³√343 = 7 cm.
8. The surface area of a cube is 150 cm². What is the length of one side?
Answer:
Explanation:
Side length = √(surface area / 6) = √(150 / 6) = 5 cm.
9. A cuboid has dimensions 8 cm by 6 cm by 4 cm. What is its diagonal length?
Answer:
Explanation:
Diagonal length = √(l² + w² + h²) = √(8² + 6² + 4²) = 10 cm.
10. The volume of a cube is 512 cm³. What is the total surface area?
Answer:
Explanation:
Side length = ³√512 = 8 cm. Surface area = 6 × 8² = 384 cm².
11. A cuboid has a volume of 450 cm³. If its length and width are 15 cm and 5 cm, what is its height?
Answer:
Explanation:
Height = volume / (length × width) = 450 / (15 × 5) = 6 cm.
12. The surface area of a cube is 600 cm². What is its volume?
Answer:
Explanation:
Side length = √(600 / 6) = 10 cm. Volume = 10³ = 1000 cm³.
13. A cube's volume increases by 125 cm³ when the length of each side is increased by 1 cm. What was the original side length?
Answer:
Explanation:
Let the original side length be x. Then (x + 1)³ – x³ = 125. Solving this gives x = 5 cm.
14. If the length of a cuboid is doubled and its width and height are halved, what happens to its volume?
Answer:
Explanation:
New volume = 2l × (1/2)w × (1/2)h = original volume.
15. A cuboid is 10 cm long, 8 cm wide, and 6 cm high. What is the length of the longest rod that can fit inside the cuboid?
Answer:
Explanation:
The longest rod = √(l² + w² + h²) = √(10² + 8² + 6²) = 14 cm.
16. The ratio of dimensions of a cuboid is 1:2:3 and its volume is 216 cm³. What is the length of its longest side?
Answer:
Explanation:
Let dimensions be x, 2x, 3x. Volume = x × 2x × 3x = 6x³ = 216. Solving gives x = 3, so longest side = 3x = 9 cm.
17. A cube's side is increased by 20%. What is the percentage increase in its volume?
Answer:
Explanation:
New volume = (1.2 side)³ = 1.728 original volume. Percentage increase = (1.728 – 1) × 100 = 72.8%.
18. A cuboid has a total surface area of 94 cm². If its length is 5 cm and width is 4 cm, what is its height?
Answer:
Explanation:
Surface area = 2(lw + lh + wh). Solving for h gives h = 3 cm.
19. The length of a cube is increased by 50%. What is the increase in its surface area?
Answer:
Explanation:
New surface area = (1.5 side)² × 6 = 2.25 original surface area. Increase = (2.25 – 1) × 100 = 125%.
20. A cuboid's length is 4 times its height and twice its width. If its volume is 64 cm³, what is its width?
Answer:
Explanation:
Let width = x, length = 4x, height = 2x. Volume = 4x × 2x × x = 64. Solving gives x = 2 cm.
21. The surface area of a cube is 54 cm². What is the length of one of its diagonals?
Answer:
Explanation:
Side length = √(54 / 6) = 3 cm. Diagonal = side × √3 = 3√3 cm.
22. A cuboid is 8 cm long, 5 cm wide, and 2 cm high. What is its surface area?
Answer:
Explanation:
Surface area = 2(lw + lh + wh) = 2(8×5 + 8×2 + 5×2) = 76 cm².
23. The side of a cube is tripled. How many times does its volume increase?
Answer:
Explanation:
New volume = (3 side)³ = 27 original volume.
24. A cuboid's dimensions are increased by 10%, 20%, and 30%. What is the percentage increase in its volume?
Answer:
Explanation:
New volume = 1.1 × 1.2 × 1.3 original volume = 1.716 original volume. Increase = (1.716 – 1) × 100 = 71.6% ≈ 72%.
25. If a cube has a volume of 27 cm³, what is the area of one of its faces?
Answer:
Explanation:
Side length = ³√27 = 3 cm. Area of one face = side² = 3² = 9 cm².