Cube and Cuboid MCQ & Objective Questions
The concepts of Cube and Cuboid are fundamental in geometry and play a significant role in various examinations. Understanding these shapes not only enhances your spatial reasoning but also boosts your confidence in solving related MCQs and objective questions. Practicing Cube and Cuboid MCQ questions helps in reinforcing your knowledge and prepares you for important questions that frequently appear in school and competitive exams.
What You Will Practise Here
Definitions and properties of Cube and Cuboid
Formulas for surface area and volume
Diagrams illustrating Cube and Cuboid
Real-life applications of Cube and Cuboid
Common problems and their solutions
Comparison between Cube and Cuboid
Practice questions with detailed explanations
Exam Relevance
Cube and Cuboid are essential topics in the curriculum of CBSE, State Boards, and competitive exams like NEET and JEE. Questions related to these shapes often appear in various formats, including direct calculations of volume and surface area, as well as application-based problems. Familiarity with Cube and Cuboid objective questions with answers will help you tackle these questions effectively, ensuring you score well in your exams.
Common Mistakes Students Make
Confusing the formulas for surface area and volume
Overlooking the dimensions when calculating volume
Misinterpreting the properties of Cube and Cuboid
Neglecting to draw diagrams for better visualization
FAQs
Question: What is the formula for the volume of a Cube?Answer: The volume of a Cube is calculated using the formula V = a³, where 'a' is the length of one side.
Question: How do you find the surface area of a Cuboid?Answer: The surface area of a Cuboid is given by the formula SA = 2(lb + bh + hl), where 'l', 'b', and 'h' are the length, breadth, and height respectively.
Now that you are equipped with the essential concepts of Cube and Cuboid, it's time to put your knowledge to the test! Solve practice MCQs and solidify your understanding to excel in your exams.
Q. A cube and a cuboid have the same volume of 27 cm³. What is the side length of the cube?
A.
3 cm
B.
4 cm
C.
5 cm
D.
6 cm
Show solution
Solution
The volume of a cube is side³. Therefore, side = ³√27 = 3 cm.
Correct Answer:
A
— 3 cm
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Q. A cube's edge is increased by 50%. What is the percentage increase in its volume?
A.
50%
B.
100%
C.
125%
D.
150%
Show solution
Solution
Volume increases by the cube of the increase in edge length. (1.5)³ = 3.375, which is a 237.5% increase.
Correct Answer:
C
— 125%
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Q. A cuboid has a length of 10 cm, a width of 4 cm, and a height of 5 cm. What is its volume?
A.
200 cm³
B.
150 cm³
C.
100 cm³
D.
250 cm³
Show solution
Solution
Volume = length × width × height = 10 × 4 × 5 = 200 cm³.
Correct Answer:
A
— 200 cm³
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Q. A cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its surface area?
A.
30 cm²
B.
62 cm²
C.
38 cm²
D.
40 cm²
Show solution
Solution
The surface area of a cuboid is calculated as 2(lw + lh + wh). Here, 2(5*3 + 5*2 + 3*2) = 2(15 + 10 + 6) = 62 cm².
Correct Answer:
C
— 38 cm²
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Q. A cuboid has a length of 5 cm, width of 3 cm, and height of 2 cm. What is its volume?
A.
30 cm³
B.
15 cm³
C.
10 cm³
D.
25 cm³
Show solution
Solution
The volume of a cuboid is calculated as length × width × height. Therefore, 5 cm × 3 cm × 2 cm = 30 cm³.
Correct Answer:
B
— 15 cm³
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Q. A cuboid has a volume of 120 cm³ and a height of 5 cm. What is the area of its base?
A.
20 cm²
B.
24 cm²
C.
30 cm²
D.
40 cm²
Show solution
Solution
Volume = base area × height, so base area = Volume / height = 120 cm³ / 5 cm = 24 cm².
Correct Answer:
B
— 24 cm²
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Q. Choose the correct idiom that means 'to be in a difficult situation'.
A.
in a pickle
B.
on cloud nine
C.
under the weather
D.
in the same boat
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Solution
'In a pickle' means to be in a difficult or troublesome situation.
Correct Answer:
A
— in a pickle
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Q. Choose the correct idiom that means to 'make a situation worse':
A.
Add fuel to the fire
B.
Bite the bullet
C.
Break the ice
D.
Hit the nail on the head
Show solution
Solution
The idiom 'add fuel to the fire' means to make a bad situation worse.
Correct Answer:
A
— Add fuel to the fire
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Q. Choose the correct idiom to complete the sentence: 'He was in a tight ______ when he had to choose between two equally good offers.'
A.
spot
B.
cube
C.
corner
D.
box
Show solution
Solution
'In a tight corner' is an idiom meaning to be in a difficult situation.
Correct Answer:
C
— corner
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Q. Choose the correct idiom to complete the sentence: 'He was in a tight ______ when he had to choose between the two jobs.'
A.
cube
B.
spot
C.
corner
D.
place
Show solution
Solution
The idiom 'in a tight corner' means being in a difficult situation.
Correct Answer:
C
— corner
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Q. Choose the correct idiom to complete the sentence: 'He was in a _____ when he realized he had forgotten his presentation.'
A.
tight spot
B.
smooth sailing
C.
clear sky
D.
open book
Show solution
Solution
'Tight spot' means being in a difficult situation, which fits the context.
Correct Answer:
A
— tight spot
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Q. If a cube has a side length of 4 cm, what is its volume?
A.
16 cm³
B.
64 cm³
C.
48 cm³
D.
32 cm³
Show solution
Solution
The volume of a cube is calculated as side³. Therefore, 4 cm × 4 cm × 4 cm = 64 cm³.
Correct Answer:
B
— 64 cm³
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Q. If a cube has a surface area of 150 cm², what is the length of one side?
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
Surface area = 6s². Therefore, 150 = 6s², s² = 25, s = 5 cm.
Correct Answer:
B
— 6 cm
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Q. If a cube's edge is increased by 50%, what is the new volume compared to the original?
A.
Increased by 50%
B.
Increased by 125%
C.
Increased by 100%
D.
Increased by 200%
Show solution
Solution
If the edge is increased by 50%, the new edge length is 1.5 times the original. The volume increases by (1.5)³ = 3.375 times, which is an increase of 237.5%.
Correct Answer:
B
— Increased by 125%
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Q. If a cube's edge is increased by 50%, what is the percentage increase in its volume?
A.
50%
B.
100%
C.
125%
D.
150%
Show solution
Solution
Increasing the edge by 50% results in a volume increase of 125%.
Correct Answer:
C
— 125%
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Q. If a cube's side is doubled, how does its volume change?
A.
doubles
B.
triples
C.
quadruples
D.
increases eightfold
Show solution
Solution
If the side is doubled, the new volume is (2s)³ = 8s³, which is eight times the original volume.
Correct Answer:
D
— increases eightfold
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Q. If a cube's surface area is 150 cm², what is the length of one side?
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
Surface area of a cube = 6s², so 6s² = 150 cm², thus s² = 25 cm², and s = 5 cm.
Correct Answer:
B
— 6 cm
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Q. If a cube's volume is 125 cm³, what is the length of one side?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
The side length of a cube can be found by taking the cube root of the volume. The cube root of 125 cm³ is 5 cm.
Correct Answer:
A
— 5 cm
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Q. If a cube's volume is 27 cm³, what is the length of one side?
A.
3 cm
B.
4 cm
C.
5 cm
D.
6 cm
Show solution
Solution
The side length is the cube root of the volume. Thus, side = ³√27 = 3 cm.
Correct Answer:
A
— 3 cm
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Q. If a cuboid has a length of 10 cm, a width of 5 cm, and a height of 1 cm, what is its volume?
A.
50 cm³
B.
100 cm³
C.
25 cm³
D.
75 cm³
Show solution
Solution
The volume of a cuboid is calculated as length × width × height. Therefore, 10 cm × 5 cm × 1 cm = 50 cm³.
Correct Answer:
A
— 50 cm³
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Q. If a cuboid has a length of 5 cm, width of 3 cm, and height of 2 cm, what is its volume?
A.
30 cm³
B.
15 cm³
C.
10 cm³
D.
25 cm³
Show solution
Solution
The volume of a cuboid is calculated as length × width × height. Therefore, 5 × 3 × 2 = 30 cm³.
Correct Answer:
B
— 15 cm³
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Q. If a cuboid has a volume of 120 cm³ and a height of 5 cm, what is the area of its base?
A.
20 cm²
B.
24 cm²
C.
30 cm²
D.
15 cm²
Show solution
Solution
Volume = base area × height. Therefore, base area = Volume / height = 120 cm³ / 5 cm = 24 cm².
Correct Answer:
B
— 24 cm²
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Q. If a cuboid has dimensions 2 cm, 3 cm, and 4 cm, what is the length of its longest side?
A.
2 cm
B.
3 cm
C.
4 cm
D.
5 cm
Show solution
Solution
The longest side of the cuboid is 4 cm.
Correct Answer:
C
— 4 cm
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Q. If a cuboid has dimensions of 2 cm, 3 cm, and 4 cm, what is its total surface area?
A.
24 cm²
B.
28 cm²
C.
20 cm²
D.
18 cm²
Show solution
Solution
The surface area of a cuboid is calculated as 2(lw + lh + wh). Here, 2(2*3 + 2*4 + 3*4) = 24 cm².
Correct Answer:
A
— 24 cm²
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Q. If the length of a cube is doubled, how does its volume change?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It increases eightfold
Show solution
Solution
If the side length is doubled, the new volume is (2s)³ = 8s³, which is eight times the original volume.
Correct Answer:
D
— It increases eightfold
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Q. If the length of a cuboid is doubled, what happens to its volume?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
Show solution
Solution
If the length is doubled, the volume increases by a factor of 2 (length) × 1 (width) × 1 (height) = 2 times the original volume.
Correct Answer:
D
— It quadruples
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Q. If the phrase 'to think outside the box' is used, what does it imply?
A.
To be conventional
B.
To be creative
C.
To be lazy
D.
To be confused
Show solution
Solution
The phrase means to think creatively and not be limited by traditional ideas.
Correct Answer:
B
— To be creative
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Q. If the phrase 'to think outside the box' is used, which shape is implied?
A.
cube
B.
sphere
C.
pyramid
D.
cuboid
Show solution
Solution
The phrase implies thinking beyond conventional boundaries, often represented by a cube.
Correct Answer:
A
— cube
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Q. If the surface area of a cube is 150 cm², what is the length of one side?
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
The surface area of a cube is 6 × side². Therefore, side² = 150 cm² / 6 = 25 cm², so side = 5 cm.
Correct Answer:
B
— 6 cm
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Q. What is the relationship between the surface area and volume of a cube?
A.
Surface area is always greater
B.
Volume is always greater
C.
They are equal
D.
Surface area increases faster than volume
Show solution
Solution
As the side length increases, the volume (s³) increases faster than the surface area (6s²).
Correct Answer:
B
— Volume is always greater
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