Cube MCQ Quiz - Objective Question with Answer for Cube - Download Free PDF
Last updated on Jun 6, 2025
Latest Cube MCQ Objective Questions
Cube Question 1:
A cubical tank with side 50 cm is full of water. If 61 litres of water is taken out of it, the level of water in the tank will drop by :
Answer (Detailed Solution Below)
Cube Question 1 Detailed Solution
Given:
Side of cubical tank = 50 cm
Volume of water taken out = 61 litres = 61000 cm3
Formula used:
Volume of water removed = Area of base × Drop in water level
Area of base = Side × Side
Calculation:
Area of base = 50 × 50 = 2500 cm2
Volume of water removed = Area of base × Drop in water level
⇒ 61000 = 2500 × Drop in water level
⇒ Drop in water level = 61000 ÷ 2500
⇒ Drop in water level = 24.4 cm
∴ The correct answer is option (1).
Cube Question 2:
If the surface area of a cube is 1536 cm², then its volume is:
Answer (Detailed Solution Below)
Cube Question 2 Detailed Solution
Given:
The surface area of a cube = 1536 cm2
Formula used:
Surface Area of a Cube = 6a2
Volume of a Cube = a3
Where, a = side of the cube
Calculation:
6a2 = 1536
⇒ a2 = 1536 ÷ 6
⇒ a2 = 256
⇒ a = √256
⇒ a = 16 cm
Now, Volume = a3
⇒ Volume = 16 × 16 × 16
⇒ Volume = 4096 cm3
∴ The correct answer is option (1).
Cube Question 3:
The edges of 3 cubes of a metal are 3 cm, 4 cm and 5 cm. They are melted and recasted into a single new cube. The edge of the new cube is
Answer (Detailed Solution Below)
Cube Question 3 Detailed Solution
Given:
Edge of first cube = 3 cm
Edge of second cube = 4 cm
Edge of third cube = 5 cm
All cubes are melted and recasted into a single cube.
Formula used:
Volume of a cube = (Edge)3
Total volume of the new cube = Sum of volumes of three cubes
Edge of the new cube = \(\sqrt[3]{\text{Total Volume}}\)
Calculation:
Volume of first cube = 33 = 27 cm3
Volume of second cube = 43 = 64 cm3
Volume of third cube = 53 = 125 cm3
Total volume = 27 + 64 + 125 = 216 cm3
Edge of the new cube = \(\sqrt[3]{216}\)
⇒ Edge of the new cube = 6 cm
∴ The correct answer is option 2.
Cube Question 4:
The volume of a cube is 6,58,503 cm³. What is twice the length (in cm) of its side?
Answer (Detailed Solution Below)
Cube Question 4 Detailed Solution
Given:
Volume of the cube (V) = 6,58,503 cm3
Formula used:
Volume of cube (V) = a3
Where, a = length of the side of the cube
Calculations:
6,58,503 = a3
⇒ a = 6,58,503(1/3)
⇒ a = 87
Twice the length of the side = 2 × a
⇒ Twice the length of the side = 2 × 87 = 174 cm.
∴ The correct answer is option (3).
Cube Question 5:
A cube of 25 cm side is divided into 125 smaller cubes of equal volume. Find the side of smaller cubes :
Answer (Detailed Solution Below)
Cube Question 5 Detailed Solution
Given:
Side of larger cube = 25 cm
Number of smaller cubes = 125
Formula used:
Volume of a cube = (Side)3
Volume of larger cube = Volume of 125 smaller cubes
Calculations:
Volume of larger cube = (Side of larger cube)3
⇒ Volume = 253 = 15625 cm3
Volume of each smaller cube = Volume of larger cube ÷ Number of smaller cubes
⇒ Volume of each smaller cube = 15625 ÷ 125 = 125 cm3
Side of smaller cube = (Volume)(1/3)
⇒ Side = 125(1/3)
⇒ Side = 5 cm
∴ The correct answer is option (3).
Top Cube MCQ Objective Questions
A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:
Answer (Detailed Solution Below)
Cube Question 6 Detailed Solution
Download Solution PDFGiven:
Each side of the cube = 8 cm
The rectangular container has a length of 16 cm, breadth of 8 cm, and height of 15 cm
Formula used:
The volume of cube = (Edge)3
The volume of a cuboid = Length × Breadth × Height
Calculation:
The volume of cube = The volume of the rectangular container with a length of 16 cm, breadth of 8 cm, and height of the water level rise
Let, the height of the water level will rise = x cm
So, 83 = 16 × 8 × x
⇒ 512 = 128 × x
⇒ x = 512/128 = 4
∴ The rise of water level (in cm) is 4 cm
Three cubes with sides in the ratio of 3 ∶ 4 ∶ 5 are melted to form a single cube whose diagonal is 18√3 cm. The sides of the three cubes are:
Answer (Detailed Solution Below)
Cube Question 7 Detailed Solution
Download Solution PDFGiven:
Three cubes with sides in the ratio of 3 ∶ 4 ∶ 5 are melted to form a single cube whose diagonal is 18√3 cm.
Concept used:
The diagonal of a cube = √3a (where a is the sides)
Calculation:
Let the s sides of the cubes will be 3x cm , 4x cm, and 5x cm
As per the question,
Volume of the new cube is
(3x)3 +( 4x)3 +( 5x)3 = 216 x3.
⇒ side is = 6x
diagonal is 6x√3
⇒ 6x√3 = 18√3
⇒ x = 3
The sides of the cubes will be 9 cm , 12 cm, and 15 cm
∴ The correct option is 2
There is wooden sphere of radius \(15√ 3\) cm. The total surface area of the largest possible cube cut out from the sphere will be:
Answer (Detailed Solution Below)
Cube Question 8 Detailed Solution
Download Solution PDFGiven:
The radius of the sphere, r = 15√3 cm
Concept:
The total surface area of a cube = 6 × (edge length)2.
Length of the main diagonal of cube = (edge length)√3
Solution:
The diameter of the sphere = Length of the main diagonal of the cube.
2 × \(15√ 3\) = a√3
a = 30 cm
Total surface area of the cube = 6 × (edge length)2
Total surface area of the cube = 6 × (30)2 = 5400 cm2.
Hence, the total surface area of the largest possible cube cut out from the sphere will be 5400 cm2.
If the sides of three cubes are in the ratio 2 : 3 : 5 and the total volume is 54880 cm3, then the length of the sides of the largest cube is
Answer (Detailed Solution Below)
Cube Question 9 Detailed Solution
Download Solution PDFFormula Used:
The volume of cube = (side)3
Calculation:
Let the sides of cubes be 2x cm, 3x cm, and 5x cm.
The volume of Cubes is (2x)3, (3x)3, (5x)3 respectively.
Total Volume = 54880 cm3
⇒(2x)3+ (3x)3 + (5x)3 = 54880
⇒8x3 + 27x3 + 125x3 = 54880
⇒ 160x3 = 54880
⇒ x3 = 54880 ÷ 160 = 343
⇒ x3 = 73
⇒ x = 7
Hence, the side of the largest cube is 5 × 7 = 35 cm.
Three cubes of metal whose edges are in the ratio 3 ∶ 4 ∶ 5 are melted down into a single cube whose diagonal is \(12\sqrt 3 \) cm. Find the edges of the smallest cube.
Answer (Detailed Solution Below)
Cube Question 10 Detailed Solution
Download Solution PDFGiven:
The ratio of the sides of three cubes = 3 ∶ 4 ∶ 5
Diagonal of the resultant cube = \(12\sqrt 3 \)
Formula used:
The volume of a cube = side3
Diagonal of a cube = \(\sqrt 3 \) side
Concept used:
if three different cubes are melted down into a single cube then the sum of the volume of the three cubes is equal to the volume of the resultant cube
Calculation:
Diagonal of a cube = side\(\sqrt 3 \)
\(12\sqrt 3 \) = side\(\sqrt 3 \)
Side of the resultant cube = 12 cm
The ratio of the sides of three cubes = 3 ∶ 4 ∶ 5
let the sides of the three cubes be 3x, 4x, 5x
Sum of the volume of three cubes = Volume of the resultant cube
27x3 + 64x3 + 125x3 = 123
⇒ 216x3 = 123
⇒ 216x3 = 1728
⇒ x3 = 8
⇒ x = 2
then the sides of the cube are 6cm, 8cm, 10cm
The smallest side is 6cm
The answer is 6cm
The Sum of all edges of a cube is 60 cm, then find the length of the largest rod that can be fit in the cube.
Answer (Detailed Solution Below)
Cube Question 11 Detailed Solution
Download Solution PDFGiven:
Sum of all 12 edges of cube = 60 cm
Formula:
Number of edges in a cube = 12
Diagonal (body) of cube = √3a
Calculation:
Let the side of the cube be a cm, then
12a = 60
⇒ a = 60/12
⇒ a = 5 cm
∴ Largest rod that can be fit in cube = √3a = 5√3 cm
The dimensions of a metallic cuboid are 50 cm × 40 cm × 32 cm. This cuboid is melted and recast into a cube. Find the total surface area of the cube.
Answer (Detailed Solution Below)
Cube Question 12 Detailed Solution
Download Solution PDFGiven:
Dimensions of metallic cuboid = 50 cm × 40 cm × 32 cm
The metallic cuboid is melted and recast into a cube.
Formulas used:
Volume of cuboid = length × breadth × height
Volume of cube with side 'a' = a3
Surface area of cube = 6a2
Calculation:
Volume of cuboid = Volume of cube
50 cm × 40 cm × 32 cm = a3
⇒ 2 × 52 × 5 × 23 × 25 = a3
⇒ 64000 = a3
⇒ a = ∛64000 cm3
⇒ a = 40 cm
∴ Surface area of cube = 6 × 40 × 40
⇒ 9600 cm2
The area of the floor of a cubical room is 192 m2. The length of the longest rod that can be kept in that room is :
Answer (Detailed Solution Below)
Cube Question 13 Detailed Solution
Download Solution PDFGiven:
Area of the floor of a cubical room = 192 m2
Formula used:
Diagonal of the cube = √3 × side of cube
Floor area = side2 (floor of the cube is in the shape of a square)
Calculation:
According to the question,
The floor area of the cube = side2
⇒ 192 = side2
⇒ side of cube = √192 = 8√ 3 m
Diagonal = √3 × side of the cube
⇒ √3 × 8 × √3
⇒ 8 × 3 = 24 m
∴ The length of the longest rod that can be kept in that room is 24 m.
If the edge of a cube is increased by 2 cm, the volume will increase by 488 cm3. What then will be the length of each edge of the cube?
Answer (Detailed Solution Below)
Cube Question 14 Detailed Solution
Download Solution PDFLet the length of the cube be x cm
⇒ The length after 2 cm increase = x + 2 m
⇒ Initial volume = x3
⇒ Volume after increasing side = (x + 2)3
⇒ (x + 2)3 – x3 = 488
⇒ x3 + 6x2 + 12x + 8 – x3 = 488
⇒ 6x2 + 12x – 480 = 0
⇒ x2 + 2x – 80 = 0
⇒ (x – 8) (x + 10) = 0
⇒ x = 8, -10
⇒ x = 8 cmThe total surface area of a cube is 2904 cm2. What is the volume of this cube?
Answer (Detailed Solution Below)
Cube Question 15 Detailed Solution
Download Solution PDFLet the side of the cube is a.
The total surface area of the cube = 6a2
⇒ 6a2 = 2904
⇒ a2 = 2904/6 = 484
⇒ a = 22 cm
volume of this cube = a3 = 223 = 10648 cm3