Cube and Cuboid
1. How many small cubes are there in a cube of side 4 cm, if it is cut into cubes of side 1 cm?
A. 16
B. 32
C. 64
D. 128
C. 64
2. A cube has a volume of 216 cm³. What is the length of its edge?
A. 4 cm
B. 5 cm
C. 6 cm
D. 8 cm
C. 6 cm
3. The total surface area of a cube is 150 cm². What is the length of its edge?
A. 5 cm
B. 6 cm
C. 7 cm
D. 8 cm
A. 5 cm
4. How many faces does a cuboid have?
A. 4
B. 6
C. 8
D. 12
B. 6
5. A cuboid has length 8 cm, breadth 6 cm, and height 4 cm. What is its volume?
A. 160 cm³
B. 176 cm³
C. 192 cm³
D. 200 cm³
C. 192 cm³
6. A cube of side 4 cm is cut into 1 cm cubes. How many small cubes will have paint on exactly two faces?
A. 8
B. 16
C. 24
D. 32
C. 24
7. How many cubes are obtained when a 6 cm cube is cut into 2 cm cubes?
A. 27
B. 64
C. 216
D. 125
A. 27
8. A cuboid of dimensions 5×6×7 cm is painted and cut into 1 cm cubes. How many cubes have no face painted?
A. 60
B. 90
C. 120
D. 150
A. 60
9. 125 identical cubes are arranged to form a larger cube. How many cubes are completely hidden from view?
A. 8
B. 27
C. 64
D. 97
B. 27
10. A cube is painted red on two opposite faces, blue on two other opposite faces, and green on the remaining faces. It is then cut into 64 smaller cubes. How many cubes have only one face painted green?
A. 4
B. 8
C. 12
D. 16
B. 8
11. A cube of side 10 cm is cut into 2 cm cubes. What is the percentage increase in total surface area?
A. 200%
B. 400%
C. 800%
D. 1500%
B. 400%
12. A cuboid of dimensions 8×12×10 cm is cut into 2 cm cubes. How many cubes have exactly two faces painted?
A. 36
B. 56
C. 84
D. 128
A. 36
13. If a cube is cut into 27 equal smaller cubes, by what factor does the total surface area increase?
A. 2 times
B. 3 times
C. 6 times
D. 9 times
B. 3 times
14. In a 4×4×4 cube made of 64 unit cubes, how many cubes are passed through by a space diagonal?
A. 4
B. 8
C. 12
D. 16
A. 4
15. What is the minimum number of cuts required to cut a 5×5×5 cube into 125 unit cubes if pieces can be rearranged between cuts?
A. 6
B. 9
C. 12
D. 15
A. 6