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
➩ 6z2 = z3
➩ 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) 14x2
b) 16x2
c) 18x2
d) 12x2
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)
= 6x2 + 2x2 + 6x2
= 14x2 cm2
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 = a3
= 93
= 729 m3
Three – fourth volume = (3 / 4) * 729
= 546.75 m3
Now, 1m3 = 1000L
Thus, 546.75 m3 = 546750 L.
4. What will be the volume of a rectangular tank having base area 84 m2 and height as 5 m?
a) 420 m3
b) 460 m3
c) 520 m3
d) 550 m3
View Answer
Explanation: Given,
Base area = 84 m2, Height = 5 m
Volume = Base area * Height
= 84 m2 * 5 m
= 420 m3
5. The lateral surface area of a cube is 81 m2. What will be the volume of this cube?
a) 625 m3
b) 590 m3
c) 729 m3
d) 780 m3
View Answer
Explanation: Given,
Lateral surface area = 81 m2.
Let the side be a m.
➩ a2 = 81 m2
➩ a = 9 m
Volume = a3 = (9m)3
= 729 m3
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 = 6a2.
= 6 * (6)2
= 216 m2
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 m3 = Area of base * height
343 m3 = Area of base * 7 m
49 m2 = 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 cm3.
Let the side of the cube = s cm
Volume of cube = s3
➩ s3 = 512 cm3
➩ 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 cm3
Volume of packet = 15 * volume of small cuboidal box
= 15 * 512 cm3
= 7680 cm3
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 m3
Volume of smaller cube = 2 * 2 * 2 m3
= 8 m3
Number of smaller cubes = Volume of larger cuboid / Volume of smaller cube
= 64 m3 / 8 m3
= 8
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