CTS Practice Cube Questions
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Below are sample cube questions to practice for CTS and other similar papers. To answer these types of questions, we would recommend you to remember certain formulas. (These formulas are given along with the solutions). Hope these help.
Question 1
Ramesh brought a 9 cm cube painted on all its sides (outside) with red paint and showed it to Suresh. Suresh was happy on seeing the cube. The cube was divided into small cubes of 1 cm each. Ramesh posed the following questions to Suresh and Suresh was perplexed to get the answers.
1) How many small cubes of 1 cm size will be there?
A) 343 B) 216 C) 729 D) 512
Answer : C) 729
Formula = n3 = 93 = 729 ( Number of cubes of 1 cm is same as the volume of the cube in cubic cm)
2) How many small cubes of 1 cm size will have only two surfaces painted?
A) 48 B) 84 c) 84 d) none of these
Answer : B) 84
Formula - Blocks painted on 2 surfaces - 12(n -2)
12(9-2) = 12 x 7 = 84
3) How many small cubes of 1 cm size will have one surface painted?
a) 324 b) 484 c) 516 d) 294
Answer : d) 294
Formula - Blocks painted on one surface only - 6 (n – 2) 2
= 6 ( 9 - 2 )2 = 6 x 72 = 294
4) How many small cubes will have all its surfaces unpainted?
a) 216 b) 125 c) 343 d) none of these
Answer : c) 343
Formula - Blocks unpainted on all sides - (n - 2)3
(9-2)3 = 343
5) How many small cubes will have their three sides painted?
a) 16 b) 12 c) 8 d) 24
Answer : c) 8
Formula small cubes painted on 3 surfaces – it is always 8.(Small cubes at the edge on top four and at bottom four.)
Question 2
A cube of 6 cm size was brought in. It was cut into small cubes of 1 cm each. What is the percentage increase in the surface area after such cutting?
A) 400% B) 300% C) 200% D) 500%
Answer : D) 500%
Solution :
Volume of 6 cm cube = 216 cc. When it is cut into 1 cm cube, the volume of each of the cubes = 1cc
Hence, there will be 216 such cubes. Surface area of small cubes = 6 (12) = 6 sqcm.
Therefore, the surface area of 64 such cubes = 216 * 6 = 1296 sqcm.
The surface area of the large cube = 6(62) = 6*36 = 216.
% increase =( 1296 - 216) / 216 X 100 = 500%
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