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
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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 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
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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
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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 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
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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 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
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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 _____ when he realized he had forgotten his presentation.'
A.
tight spot
B.
smooth sailing
C.
clear sky
D.
open book
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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
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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
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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%
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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 side is doubled, how does its volume change?
A.
doubles
B.
triples
C.
quadruples
D.
increases eightfold
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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
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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 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
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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 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 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
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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, which shape is implied?
A.
cube
B.
sphere
C.
pyramid
D.
cuboid
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Solution
The phrase implies thinking beyond conventional boundaries, often represented by a cube.
Correct Answer:
A
— cube
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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
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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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Q. What is the relationship between the volume of a cube and a cuboid with the same height and base area?
A.
The cube has a greater volume
B.
The cuboid has a greater volume
C.
They have the same volume
D.
It cannot be determined
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Solution
A cube with the same height and base area will always have a greater volume than a cuboid unless the cuboid is also a cube.
Correct Answer:
A
— The cube has a greater volume
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Q. What is the term for a three-dimensional shape with six rectangular faces?
A.
cube
B.
sphere
C.
cuboid
D.
pyramid
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Solution
A cuboid is defined as a three-dimensional shape with six rectangular faces.
Correct Answer:
C
— cuboid
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Q. What is the total number of edges in a cube?
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Solution
A cube has 12 edges.
Correct Answer:
B
— 12
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Q. What is the total number of edges in a cuboid?
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Solution
A cuboid has 12 edges.
Correct Answer:
B
— 12
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Q. Which idiom best describes a situation where something is perfectly aligned or fitting?
A.
fits like a glove
B.
out of the blue
C.
cut corners
D.
in the same boat
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Solution
'Fits like a glove' means something fits perfectly, similar to how a cube fits into a cubical space.
Correct Answer:
A
— fits like a glove
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Q. Which of the following is a synonym for 'cuboid'?
A.
rectangular prism
B.
sphere
C.
cone
D.
cylinder
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Solution
A cuboid is also known as a rectangular prism.
Correct Answer:
A
— rectangular prism
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Q. Which of the following is a synonym for 'rectangular'?
A.
cuboidal
B.
square
C.
cubic
D.
linear
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Solution
'Cuboidal' refers to a shape that has a rectangular form, making it a synonym.
Correct Answer:
A
— cuboidal
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Q. Which of the following is an antonym of 'cubical'?
A.
spherical
B.
rectangular
C.
triangular
D.
flat
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Solution
'Cubical' refers to a shape with equal dimensions, while 'spherical' refers to a round shape, making it an antonym.
Correct Answer:
A
— spherical
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Q. Which of the following is an antonym of 'cuboid'?
A.
rectangle
B.
sphere
C.
triangle
D.
circle
Show solution
Solution
A sphere is a three-dimensional shape that is not a cuboid.
Correct Answer:
B
— sphere
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