Last updated on Jan 24, 2023

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:

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
5. Not Attempted

Option 4 : 35 cm

#### Cube Question 1 Detailed Solution

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.

#### Cube Question 2:

The dimensions of an ice compartment in a refrigerator . How many ice cubes will it hold, if each ice cube is 2 cm on its edge?

1. 24
2. 80
3. 20
4. 40
5. Not Attempted

Option 3 : 20

#### Cube Question 2 Detailed Solution

Given:

Dimensions of an ice compartment; L = 8 cm, B = 5 cm, H = 4 cm

Dimensions of an ice cube; l = b = h = 2 cm

Concept Used:

Volume of cuboid = L × B × H

Volume of cube = Side3

Number of ice cubes = Volume of cuboid ÷ Volume of cube

Calculation:

⇒ Volume of cuboid = 8 × 5 × 4 = 160 cm3

⇒ Volume of cube = 23 = 8 cm3

⇒ Required number of ice cubes $$=\frac{160}{8}=20$$
Therefore, the ice compartment can hold 20 such ice cubes.

#### Cube Question 3:

If the volume of a cube is $$192 \sqrt 3$$ cubic cm, then the length of its diagonal is:

1. 16 cm
2. 14 cm
3. 13 cm
4. 12 cm
5. Not Attempted

Option 4 : 12 cm

#### Cube Question 3 Detailed Solution

Given:

Volume of cube = 192√3 cubic cm

Formula used:

Volume of cube = a3

Where a = side of the cube

Length of the diagonal of the cube = √3 × a

Calculation:

Let the side of the cube be 'a' cm

Volume = 192√3

⇒ a3 = 192√3

⇒ a = (192√3)1/3 = (4 × 4 × 4 × 3 × √3)1/3

⇒ a = 4 × (3√3)1/3

Diagonal of the cube = √3 × a

⇒ √3 × 4 × (3√3)1/3

⇒ √3 × 4 × [(√3)3]1/3

⇒ 12 cm

∴ The length of the diagonal of the cube is 12 cm.

#### Cube Question 4:

Three cubes of a metal whose edges are in the ratio 3 ∶ 4 ∶ 5 are melted and converted into a single cube whose diagonal is 12√3 cm. Find the edges of the three cubes.

1. 6 units, 8 units, 11 units
2. 6 units, 18 units, 10 units
3. 16 units, 8 units, 10 units
4. 6 units, 8 units, 10 units

Option 4 : 6 units, 8 units, 10 units

#### Cube Question 4 Detailed Solution

Given:

Edges = 3 : 4 : 5

Formula used:

Diagonal = $$\sqrt3$$ x side

Volume(Cube) =  side x side x side

Solution:

Let,

Edge of three cubes be 3m, 4m and 5m respectively.

Volumes of the three cubes will be 27m3, 64m3, and 125m3 respectively.

Volume of larger cube = (27 + 64 + 125)m3

Volume = 216m3

Side of larger cube = 6m

Diagonal of larger cube = $$\sqrt3$$ x 6m = 12$$\sqrt3$$

m = 2

Side of three cubes are

3m = 3 x 2 = 6 units

4m = 4 x 2 = 8 units

5m = 5 x 2 = 10 units

Hence, the correct option is 4.

#### Cube Question 5:

If the side of a cube is 5 cm. find then length of the largest rod that can be fitted inside that cube ?

1. 43
2. 53
3. 33
4. 63

Option 2 : 53

#### Cube Question 5 Detailed Solution

Given:

Length of the side of a cube = 5 cm.

Calculation:

We know that the largest rod that can be fitted inside a cude is = a 3

where a is the side of the cube.

so the largest rod is 5 3.

## Top Cube MCQ Objective Questions

#### Cube Question 6

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

Option 2 : 4

#### Cube Question 6 Detailed Solution

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

#### Cube Question 7

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

Option 4 : 5√3 cm

#### Cube Question 7 Detailed Solution

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

#### Cube Question 8

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

Option 4 : 10648 cm3

#### Cube Question 8 Detailed Solution

Let 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

#### Cube Question 9

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

Option 3 : 6 cm

#### Cube Question 9 Detailed Solution

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

#### Cube Question 10

Three metal cubes whose edges measure 3 cm, 4 cm, and 5 cm respectively are melted to form a single cube, find its edge.

1. 15 cm
2. 12 cm
3. 6 cm
4. none of these

Option 3 : 6 cm

#### Cube Question 10 Detailed Solution

Given:

Sides of cubes =  3 cm, 4 cm and 5 cm

Concept used:

​Volume of single cube = Total volume of three melted cubes

Formula used:

Volume of cube = a3

where, a = side of cube

Calculations:

Volume of single cube = Total volume of three cubes

⇒ a3 = x3 + y3 + z3

⇒ a3 = 33 + 43 + 53

⇒ a3 = 27 + 64 + 125

⇒ a3 = 216

⇒ a = 6 cm

∴ The edge of final cube is 6 cm.

#### Cube Question 11

If the volumes of two cubes are in the ratio of 64 : 125, then what is the ratio of their total surface areas?

1. 9 : 16
2. 4 : 5
3. 16 : 25
4. 64 : 125

Option 3 : 16 : 25

#### Cube Question 11 Detailed Solution

Concept used:

• Volume of cube = (side)3

• Total surface area of a cube = 6 × (side)2

Calculation:

Let the edge length of two cubes be x & y respectively

According to the question,

⇒ x3 : y3 = 64 : 125

⇒ x : y = 4 : 5

Required ratio of total surface area = 6x2 : 6y2

= 42 : 52

= 16 : 25

∴ The ratio of their total surface area 16 : 25

#### Cube Question 12

Three cubes of edges 6 cm, 8 cm and 10 cm respectively are melted and without any loss of metal moulded into a single cube. The edge of the new cube will be:

1. 25 cm
2. 12 cm
3. 20 cm
4. None of the above

Option 2 : 12 cm

#### Cube Question 12 Detailed Solution

Concept:

Volume of a cube = edge3

Calculation:

Let the edge of new cube be a cm.

Volume of the new cube = Sum of the volumes of all the three smaller cubes

⇒ a3 = 63 + 83 + 103

⇒ a3 = 216 + 512 + 1000

⇒ a3 = 1728

⇒ a3 = 123

⇒ a = 12 cm

Hence, the edge of new cube is 12 cm.

#### Cube Question 13

The space diagonal of a cube measures 8√3 cm. What is the volume of the cube?

1. 512 cm3
2. 512√3 cm3
3. 1536√3 cm3
4. 1536 cm3

Option 1 : 512 cm3

#### Cube Question 13 Detailed Solution

Given:

The space diagonal of a cube = 8√3 cm

Formula used:

Diagonal of cube = √3a

Volume of cube = a3

Calculation:

According to the question

⇒ √3a = 8√3 cm

⇒ a = 8 cm

Now,

Volume of the cube = (8)3

⇒ 8 × 8 × 8 = 512 cm3

∴ The volume of the cube is 512 cm3

#### Cube Question 14

The dimensions of a metallic cuboid are 50 cm × 40 cm × 32 cm. This cuboid is melted and recast into a cube. Find the surface area of the cube.

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

Option 1 : 9,600 cm2

#### Cube Question 14 Detailed Solution

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

#### Cube Question 15

A box with inside measurements 60 cm × 30 cm ×  24 cm is full of wooden cubes of the same size. If the number of cubes is 25, then the side (in cm) of each cube is

1. 6
2. 9
3. 12
4. 18

Option 3 : 12

#### Cube Question 15 Detailed Solution

Given:

Measurements of box = 60 cm × 30 cm ×  24 cm

Number of cubes = 25

Formula used:

Volume of cuboid = Length × Breadth × Height

Volume of cube = (Side of cube)3

Calculations:

Total volume of the box = 60 × 30 × 24

⇒ 43200

Volume of each cube = Total volume of box / Number of cubes

⇒ 43200/25

⇒ 1728 cm3

(Side of cube)3 = 1728

Side of cube = 12 cm

∴ The side of each cube is 12 cm
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