Cube MCQ Quiz - Objective Question with Answer for Cube - Download Free PDF

Last updated on Jun 6, 2025

Testbook provides Cube Question Answers with easy and logical explanations which will help the candidates easily attempt the question in Bank PO, IBPS PO, SBI PO, RRB PO, RBI Assistant, LIC,SSC, MBA - MAT, XAT, CAT, NMAT, UPSC, NET exams. Important and frequently asked Cube MCQs Quiz have also been included so that the candidates know the type of questions they can expect from this section. Start practising the Cube Objective Questions today!

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 :

  1. 24.4 cm
  2. 25 cm 
  3. 25.6 cm
  4. 30 cm 

Answer (Detailed Solution Below)

Option 1 : 24.4 cm

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: 

  1. 4096 cm³
  2. 512 cm³
  3. 729 cm³
  4. 1728 cm³

Answer (Detailed Solution Below)

Option 1 : 4096 cm³

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

  1. 12 cm
  2. 6 cm
  3. 14 cm
  4. None of these

Answer (Detailed Solution Below)

Option 2 : 6 cm

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?

  1. 84
  2. 86
  3. 174
  4. 166

Answer (Detailed Solution Below)

Option 3 : 174

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 :

  1. 2 cm
  2. 3 cm 
  3. 5 cm
  4. 6 cm

Answer (Detailed Solution Below)

Option 3 : 5 cm

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:

  1. 6
  2. 4
  3. 2
  4. 5

Answer (Detailed Solution Below)

Option 2 : 4

Cube Question 6 Detailed Solution

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Given:

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 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:

  1. 21 cm, 28 cm and 35 cm
  2. 9 cm, 12 cm and 15 cm
  3. 18 cm, 24 cm and 30 cm
  4. 12 cm, 16 cm and 20 cm

Answer (Detailed Solution Below)

Option 2 : 9 cm, 12 cm and 15 cm

Cube Question 7 Detailed Solution

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Given:

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:

  1. 540 cm2
  2. 900 cm2
  3. 600 cm2
  4. 5,400 cm2

Answer (Detailed Solution Below)

Option 4 : 5,400 cm2

Cube Question 8 Detailed Solution

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Given:

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

  1. 14 cm
  2. 21 cm
  3. 28 cm
  4. 35 cm

Answer (Detailed Solution Below)

Option 4 : 35 cm

Cube Question 9 Detailed Solution

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Formula 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)+ (5x)3 = 54880

⇒8x+ 27x+ 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.

  1. 3 cm
  2. 8 cm
  3. 6 cm
  4. 10 cm

Answer (Detailed Solution Below)

Option 3 : 6 cm

Cube Question 10 Detailed Solution

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Given:

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

27x+ 64x+ 125x= 123

⇒ 216x= 123

⇒ 216x= 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.

  1. 6√3 cm
  2. 3√3 cm
  3. 4√3 cm
  4. 5√3 cm

Answer (Detailed Solution Below)

Option 4 : 5√3 cm

Cube Question 11 Detailed Solution

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Given:

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.

  1. 9,600 cm2
  2. 7,150 cm2
  3. 8,700 cm2
  4. 8,350 cm2

Answer (Detailed Solution Below)

Option 1 : 9,600 cm2

Cube Question 12 Detailed Solution

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Given:

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 :

  1. 18 m
  2. 22 m
  3. 24 m
  4. 26 m

Answer (Detailed Solution Below)

Option 3 : 24 m

Cube Question 13 Detailed Solution

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Given:

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?

  1. 8 cm
  2. 6 cm
  3. 9 cm
  4. 7 cm

Answer (Detailed Solution Below)

Option 1 : 8 cm

Cube Question 14 Detailed Solution

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Let 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 cm

The total surface area of a cube is 2904 cm2. What is the volume of this cube?

  1. 11748 cm3
  2. 10848 cm3
  3. 10748 cm3
  4. 10648 cm3

Answer (Detailed Solution Below)

Option 4 : 10648 cm3

Cube Question 15 Detailed Solution

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Let the side of the cube is a.
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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
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