A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, how many 1 cubic centimetre cubes will have exactly one of their faces painted?
(a) 27
(b) 42
(c) 54
(d) 142
Solution:
On each side there will be exactly nine 1 cm³ cubes that will have only one side of the face painted as shown in the diagram below.
Only the nine cubes in the centre on each face will have only one face painted. Hence the total number of cubes with one face painted will be:
Number of 1 cm³ painted only on one side = 9 × 6 = 54
Answer is (c).
✦Try This: A cube of side 8 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, how many 1 cubic centimetre cubes will have exactly one of their faces painted? (a) 216 (b) 256 (c) 288 (d) 142
The 8 cm cube if broken into 1 cm³ cubes will have 36 cubes per face which will have only one face coloured. Since there are six faces, the total number of cubes with one face painted will be = 6 × 36 = 216.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 1
A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, how many 1 cubic centimetre cubes will have exactly one of their faces painted? (a) 27 (b) 42 (c) 54 (d) 142
Summary:
A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimeter cubes, then there will be 54 one cubic centimetre cubes will have exactly one of their faces painted
☛ Related Questions:
- A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original c . . . .
- A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of max . . . .
- What is the area of the largest triangle that can be fitted into a rectangle of length L units and w . . . .