Following quiz provides Multiple Choice Questions (MCQs) related to Cube and Cuboid. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.
Q 1 - A big cube is having 15 cm portion and the tiny cubes cut out of it is having 3 cm in each portion. Then how many tiny cubes will be formed such that each face of these cubes is surrounded by other cubes?
Here x = 15/3 = 5. Such cubes can be found by following method. X – 2 = 5 - 2 = 3 and 3 × 3 × 3 = 27. So number of cubes will be formed such that each face of these cubes is surrounded by other cubes is 27.
Tiny cubes having only two faces varnished = (x - 2) × number of edges = (6 - 2) × 12 = 4 × 12 = 48. Hence option D is the answer.
Tiny cubes having only two faces varnished = (x - 2) × number of edges = (4 - 2) × 12 = 2 × 12 = 24. Hence option C is the correct answer.
Q 4 - What will be length of the portion of tiny cubes, if each portion of the original big cube is 14 cm and the cube is segmented into 343 tiny ones?
Here number of tiny cubes = 343. Cube root of 343 = 7. So x = 7 cm.
2 = (14/portion of tiny cube) or portion of tiny cube = 14/7 = 2 cm.
Q 5 - What will be length of the portion of tiny cubes, if each portion of the original big cube is 4 cm and the cube is segmented into 125 tiny ones?
Number of tiny cubes = 125. Cube root of 125 = 5. So x = 5 cm. 5 = (4/portion of tiny cube) or portion of tiny cube = 4/5 = 0.8 cm.
Q 6 - Aparajit has a cube whose each portion is of 56 cm. If he wants to cut tiny cubes of portion 7 cm each, then how many such cubes will be possible for him?
x = (56/7) = 8
So number of tiny cubes = 8 × 8 × 8 = 512. Hence option C is correct.
Q 7 - What will be length of the portion of tiny cubes, if the original big cube having each portion of 48 cm is segmented into 64 tiny ones?
Total number of cubes = 64. Cube root of 64 = 4. So x = 4 cm. 4 = (48/portion of tiny cube) or portion of tiny cube = 48/4 = 12 cm.
Q 8 - Radhamohan has a cube which has length of 15 cm, breadth of 4 cm, and height of 2 cm and is segmented into tiny cubes. How many such tiny cubes can be formed?
Number of cubes can be formed = length × breadth × height
= 15 × 4 × 2 = 120.
x = 8. So x - 2 = 8 - 2 = 6. 6 × 6 × 6 = 216.
Q 10 - A cube is segmented into 1331 equal tiny cubes. Before dividing the cube, each face of it is varnished in different colours. How many tiny cubes will be formed having more than one colour?
Here x = Cube root of 1331 = 11. More than one colour means two or more colours. So total number of cubes whose two faces are varnished is = (x - 2) × number of edges = (11 - 2) × 12 = 108. The cubes having three faces varnished are the number of corners = 8. So total number of required cubes = 108 + 8 = 116. Hence option C is the answer.