This set of Aptitude Questions and Answers (MCQs) focuses on “Cubes and Cuboids”.

1. What will be the edge length of a cube having its total surface area equal to the volume of the cube?

a) 7 units

b) 3 units

c) 6 units

d) 1 unit

View Answer

Explanation: Given,

Total surface area = Volume (for a cube)

Let the edge length = z units

According to the question

➩ 6z

^{2}= z

^{3}

➩ 6 = z

2. Three identical cubes each having a side length as x cm are joined end by end to form a cuboid. What will be the total surface area (in sq. cm) of this cuboid?

a) 14x^{2}

b) 16x^{2}

c) 18x^{2}

d) 12x^{2}

View Answer

Explanation: According to the question,

Cuboid: l = 3x, b = x, h = x

Total surface area of cuboid = 2lb + 2bh + 2hl

= 2 * (3x) * (x) + 2 * (x) * (X) + 2 * (x) * (3x)

= 6x

^{2}+ 2x

^{2}+ 6x

^{2}

= 14x

^{2}cm

^{2}

3. A cubical tank has an edge equal to 9 m. The amount of water in liters it will contain when it is three – fourth filled?

a) 439765

b) 546750

c) 678924

d) 792679

View Answer

Explanation: Given,

a = 9m

Volume of tank = a

^{3}

= 9

^{3}

= 729 m

^{3}

Three – fourth volume = (3 / 4) * 729

= 546.75 m

^{3}

Now, 1m

^{3}= 1000L

Thus, 546.75 m

^{3}= 546750 L.

4. What will be the volume of a rectangular tank having base area 84 m^{2} and height as 5 m?

a) 420 m^{3}

b) 460 m^{3}

c) 520 m^{3}

d) 550 m^{3}

View Answer

Explanation: Given,

Base area = 84 m

^{2}, Height = 5 m

Volume = Base area * Height

= 84 m

^{2}* 5 m

= 420 m

^{3}

5. The lateral surface area of a cube is 81 m^{2}. What will be the volume of this cube?

a) 625 m^{3}

b) 590 m^{3}

c) 729 m^{3}

d) 780 m^{3}

View Answer

Explanation: Given,

Lateral surface area = 81 m

^{2}.

Let the side be a m.

➩ a

^{2}= 81 m

^{2}

➩ a = 9 m

Volume = a

^{3}= (9m)

^{3}

= 729 m

^{3}

6. What will be the total surface area (in sq. m) of a cubical tank having side length as 6m?

a) 195

b) 256

c) 274

d) 216

View Answer

Explanation: Given,

a = 6m

Total surface area of tank = 6a

^{2}.

= 6 * (6)

^{2}

= 216 m

^{2}

7. A cube of edge length 7 m is converted to a cuboid of height 7 m. What will be the area (in sq. m) of the base of this cuboid so formed?

a) 49

b) 42

c) 56

d) 63

View Answer

Explanation: According to the question,

Volume of cube = Volume of cuboid

7 * 7 * 7 m

^{3}= Area of base * height

343 m

^{3}= Area of base * 7 m

49 m

^{2}= Area of base

8. What would be the edge of a cube having volume equal to the volume of a cuboid having dimensions as 16 cm * 4 cm * 8 cm?

a) 0.6m

b) 0.02m

c) 0.08m

d) 0.4m

View Answer

Explanation: Given,

Volume of cuboid = 16 cm * 4 cm * 8 cm

= 512 cm

^{3}.

Let the side of the cube = s cm

Volume of cube = s

^{3}

➩ s

^{3}= 512 cm

^{3}

➩ s = 8 cm

9. A small cubical box measures 8 cm. What will be the volume (in cubic cm) of a packet containing 20 such boxes?

a) 6940

b) 7680

c) 7550

d) 6540

View Answer

Explanation: Given,

Small cubical box = 8 cm

Volume of 1 small cuboidal box = 8 * 8 * 8

= 512 cm

^{3}

Volume of packet = 15 * volume of small cuboidal box

= 15 * 512 cm

^{3}

= 7680 cm

^{3}

10. A larger cuboid having dimensions as 2 m * 4 m * 8m is cut into a number of smaller cubes each having side length of 2 m. What will be the number of such small cubes?

a) 8

b) 4

c) 12

d) 16

View Answer

Explanation: Given,

Dimensions of larger cuboid = 2m * 4m * 8m

Volume of larger cuboid = 64 m

^{3}

Volume of smaller cube = 2 * 2 * 2 m

^{3}

= 8 m

^{3}

Number of smaller cubes = Volume of larger cuboid / Volume of smaller cube

= 64 m

^{3}/ 8 m

^{3}

= 8

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