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

Given:

Length of cuboid = 81 cm

Breadth of cuboid = 27 cm

Height of cuboid = 9 cm

Total number of smaller cubes = 729

Formula used:

Volume of cuboid = Volume of all smaller cubes

Volume of one cube = Edge³

Calculation:

Volume of cuboid = Length × Breadth × Height

⇒ Volume of cuboid = 81 × 27 × 9 = 19683 cm³

Volume of one cube = Volume of cuboid / Total number of cubes

⇒ Volume of one cube = 19683 / 729 = 27 cm³

Edge³ = Volume of one cube

⇒ Edge³ = 27

⇒ Edge = 3 cm

∴ The correct answer is option (2).

Given:

Length(L) of rectangular piece of ground = 80 m
Breadth(B) of rectangular piece of ground = 36 m 
Length(L) of pit = 40 m
Breadth(B) of pit = 18 m
Height(H) of pit = 12 m

Formula used:

Volume of earth taken out = volume of pit = L × B × H

Area of rectangle = L × B

Calculation:

According to the question,

Volume of the pit = L × B × H

⇒ 40 m × 18 m × 12 m

⇒ 8640 m³

Area of rectangular piece of ground = L × B

⇒ 80 m × 36 m

⇒ 2880 m²

Area of the base of pit = L × B 

⇒ 40 m × 18 m

⇒ 720 m²

Area of remaining portion of rectangular ground = Area of rectangular ground –Area of the base of pit.

⇒ 2880 – 720

⇒ 2160 m²

Now, the height of the level of remaining part of the ground = volume of pit/area of remaining portion of the rectangular ground

⇒ 8640/2160

⇒ 4 m

∴ The height of the land is 4 m.

Shortcut Trick

Height of pit = volume of pit/(area of ground – area of the base pit)

⇒ (40 × 18 × 12)/(80 × 36 – 40 × 18)

⇒ 4 m.

∴ The height of the land is 4 m.

Given:

Initial length of the cuboid = l

Initial breadth of the cuboid = b

Initial height of the cuboid = h

Percentage increase in length = 10%

Percentage increase in breadth = 20%

Percentage increase in height = 25%

Formula Used:

Percentage change in volume = [(New Volume - Old Volume) / Old Volume] × 100

New Volume = (New Length) × (New Breadth) × (New Height)

New Dimension = Old Dimension × (1 + Percentage Increase/100)

Calculation:

New Length = l × (1 + 10/100) = l × 1.1

New Breadth = b × (1 + 20/100) = b × 1.2

New Height = h × (1 + 25/100) = h × 1.25

New Volume = (l × 1.1) × (b × 1.2) × (h × 1.25)

New Volume = l × b × h × (1.1 × 1.2 × 1.25)

New Volume = l × b × h × 1.65

Old Volume = l × b × h

Percentage Change in Volume:

⇒ Percentage Change = [(New Volume - Old Volume) / Old Volume] × 100

⇒ Percentage Change = [((l × b × h × 1.65) - (l × b × h)) / (l × b × h)] × 100

⇒ Percentage Change = [(1.65 - 1) / 1] × 100

⇒ Percentage Change = 0.65 × 100

⇒ Percentage Change = 65%

The percentage change in the volume of the cuboid is a 65% increase.

Given:

Length increase = 20%

Breadth increase = 25%

Height increase = 30%

Formula Used:

Percentage increase in volume = [(New volume - Original volume) / Original volume] × 100

Calculation:

Let the original dimensions of the cuboid be:

Length = L, Breadth = B, Height = H

Original Volume = L × B × H

After the increase, the new dimensions will be:

New Length = L × (1 + 20/100) = 1.20L

New Breadth = B × (1 + 25/100) = 1.25B

New Height = H × (1 + 30/100) = 1.30H

New Volume = 1.20L × 1.25B × 1.30H = 1.95 × L × B × H

Percentage increase in volume = [(1.95 × L × B × H - L × B × H) / (L × B × H)] × 100

⇒ Percentage increase in volume = [(1.95 - 1) × 100] = 0.95 × 100 = 95%

∴ The percentage increase in the volume of the cuboid is 95%.

Given:

Perimeter of the cuboid = 96 m

Length (l) = 12 m

Height (h) = 7 m

Formula used:

Perimeter of a cuboid = 4(l + b + h)

Volume of a cuboid = l × b × h

Calculation:

Perimeter = 4(l + b + h)

⇒ 96 = 4(12 + b + 7)

⇒ 96 = 4(19 + b)

⇒ 96 ÷ 4 = 19 + b

⇒ 24 = 19 + b

⇒ b = 24 - 19

⇒ b = 5 m

Now, Volume = l × b × h

⇒ Volume = 12 × 5 × 7

⇒ Volume = 420 m³

∴ The correct answer is option (4).

The surface area of three faces of a cuboid sharing a vertex are 20 m², 32 m² and 40 m²,

⇒ L × B = 20 sq. Mt

⇒ B × H = 32 sq. Mt

⇒ L × H = 40 sq. Mt

⇒ L × B × B × H × L × H = 20 × 32 × 40

⇒ L²B²H² = 25600

⇒ LBH = 160

Given:

Sum of length,, breadth and height of a cuboid = 21 cm

Length of the diagonal(d) = 13 cm

Formula used:

d² = l² + b² + h²

T.S.A of cuboid = 2(lb + hb +lh)

Calculation:

⇒ l² + b² + h² = 13² = 169

According to question,

⇒ (l + b + h)² = 441

⇒ l² + b² + h² + 2(lb + hb +lh) = 441

⇒ 2(lb + hb +lh) = 441 - 169 = 272

∴ The answer is 272 cm² .

GIVEN:

Cartons having length = 48 inches and breadth = 27 inches 

The volume of cartoon = 22.5 cubic feet.

FORMULA USED :

Volume of Cuboid = Length × Breadth × Height 

CALCULATION :

Volume of carton = volume of cuboid = Length × Breadth × Height 

⇒ volume of carton = 48 × 27 × Height

∵ 1 foot = 12 inches, then 22.5 cubic feet = 22.5 × 12 × 12 ×12

⇒ 22.5 × 12 × 12 × 12 = 48 × 27 × Height     

⇒ 38,880 = 1,296 × Height 

⇒ Height = 30 inches.

∴ The height of each cartoon is 30 inches.                                     

⇒ Total water consumption of Kazipet of 1 day = 4000 × 9 = 36000 litres

⇒ Volume of cuboidal tank = 720 m³ = 720 × 1000 litres = 720000 litres

 Confusion Points
 1.You have to read the question carefully...
2.In this question the unit(thousands) of amount is already mentioned.Question wants  to answer in only amount number . so the answer will be 16 and not 16000.

Note - This is the official Question of SSC and SSC Consider 16 is the correct Answer.

Given:

Wall dimensions = 18m × 10m × 40 cm

Brick dimensions = 30 cm × 15 cm × 10 cm

Concept used:

The volume of a cuboid = Length × Breadth × Height

The volume of the wall should be equal to the volume of the total bricks required.

Calculation:

18 m = 1800 cm

10 m = 1000 cm

Volume of the wall = (1800 × 1000 × 40) cm³

Volume of each brick = (30 × 15 × 10) cm³

Now, the number of bricks required = (1800 × 1000 × 40) ÷ (30 × 15 × 10)

⇒ 16000

∴ The number of required bricks is 16 thousand.

 Confusion Points 1.You have to read the question carefully...
2.In this question the unit(thousands) of amount is already mentioned.Question wants  to answer in only amount number . so the answer will be 16 and not 16000.

Given:

The surface area of three faces = 25 m2, 32 m2 and 32 m2 

Concept used:

The surface area of one face

1.) Length × Breadth

2.) Breadth × Height

3.) Height × Length

Volume of cuboid = Length × Breadth × Height

Calculations:

We have,

⇒ Length × Breadth = 25 m²

⇒ Breadth × Height = 32 m²

⇒ Height × Length = 32 m²

Multiplying the above three equations, we get,

⇒ (Length × Breadth × Height)² = 25 × 32 × 32

Taking square root on both sides,

⇒ (Length × breadth × Height) = 5 × 32

⇒ Length × breadth × Height = 160

⇒ Volume of cuboid = 160 m³ 

∴ The volume of cuboid is 160 m³

Given:

Thickness of wood = 1 cm

Length of box = 22 cm

Breadth of box = 17 cm

Height of box = 12 cm

Calculation:

Inner length of the box = (22 − 2) = 20 cm

Inner breadth of the box = (17 − 2) = 15 cm

Inner height of the box = (12 − 2) = 10 cm

Inner volume of the box = (20 × 15 × 10) = 3000 cu. Cm

∴ Volume of cement in the box is 3000 cu. cm

Given:

Length of room = 10 m

Breadth of room = 10 m

Height of room = 5 m

Concept used:

The length of the longest rod is the diagonal of room

Diagonal of a cuboid = √[(l²) + (b²) + (h²)]

Calculation:

Diagonal of cuboid = √[(10)² + (10)² + (5)²] m

⇒ √[100 + 100 + 25] m

⇒ √[225] m

⇒ 15 m

∴ The maximum length of rod that can be placed is 15 m

Given:

Cuboid sides are in proportion to 2, 4, 5

Total surface area of the cuboid = 380cm²

Formula used:

Total surface are of the cuboid = 2( lb + bh + hl) [ where l , b, h are length , breadth and height respectively ]

Diagonal of cuboid = \(\sqrt{l^2+b^2+h^2} \)

Calculation:

Cuboid sides are in proportion to 2, 4, 5

let the sides of cuboid be 2x , 4x and 5x

Total surface area of the cuboid = 380cm²

2( lb + bh + hl) = 380

( 2x.4x + 4x.5x + 5x.2x) = 190

( 8x² + 20x² + 10x² ) = 190

38x² = 190

x² = 5

Diagonal of cuboid = \(\sqrt{l^2+b^2+h^2}\)

= \(\sqrt{(2x)^2+(4x)^2+(5x)^2}\)

= \(\sqrt{x^2(4+16+25}) \)

= \(\sqrt{5(45}) \)

= 15cm

Diagonal of the cuboid is 15cm

Answer is 15cm.

Additional Information Volume of the cuboid = Length × breadth × height

Concept used:

Volume of cuboidal box = length × breadth × height

Calculation:

Suppose the length of the box is 4x, then, its breadth will be 3x and height will be 2x.

Now, Volume = 4x × 3x × 2x = 24x³

⇒ 24x³ = 1536

⇒ x³ = 64

⇒ x = 4

Length of the box is 4x = 16 cm

∴ The the length of the box is 16 cm. 

Alternate Method

Let breadth of the box be x.

(4x/3) × x × (4x/6) =1536

⇒ 16x3/18 = 1536

⇒ x3 = 1536 × 18/16

⇒ x3 = 1728

⇒ x = 12

length = 4x/3

⇒ 4 × 12/3

⇒ 16

∴ The the length of the box is 16 cm.