18 SSC CGL Quantitative Aptitude previous year questions on Cubes and Cuboids — options free on every question; 2 include the answer & explanation free, the rest unlock with PYQ Pass.
Q1 FREE PREVIEW
PYQ
A cube is segmented into 5832 cubes. Before dividing the cube, each face of it is varnished with Blue colour. How many tiny cubes will be formed having more than 1 face coloured?
a121
b200
c169
d180
✓ Correct answer: b) 200
ExplanationHere, in the given question we have to find out the total number of tiny cubes that will be formed having two or three faces coloured.Total number of cubes having two faces coloured = (n - 2) × total number of edges in cube Total number of cubes having two faces coloured = (18 - 2) × 12 = 192 Total number of cubes having three faces coloured = Total number of corners in a cube Total number of cubes having three faces coloured = 8 So, the total number of cubes having more than one coloured = 192 + 8 = 200 Hence, 200 is the correct answer.
Q2 FREE PREVIEW
PYQ
How many cubes of 2 cm can be cut out of a cube of 12 cm length?
a216
b220
c212
d218
✓ Correct answer: a) 216
ExplanationHere, in the given question, we have to find out the total number of cubes of 2 cm that can be cut out of a cube of 12 cm length.Formula used = Volume of cube = (side)3 Let the number of cubes that can be cut from a bigger cube be N. N × Volume of smaller cube = Volume of the bigger cube So, the total number of cubes of 2 cm that can be cut out of a cube of 12 cm length is 216 .Hence, 216 is the correct answer.
Q3
PYQ
A cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides 7 cm each. Find the number of smaller cubes having only one face painted.
a100
b25
c50
d150
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Q4
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A cube of side 18 cm is painted yellow on all the faces and then cut into smaller cubes of sides 3 cm each. Find the number of smaller cubes that have only two faces painted.
a36
b48
c20
d64
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Q5
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The surface area of a cube is 864 . The volume of the cube is _______.
a1728
b2197
c1331
d729
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Q6
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A cube of side 12cm is painted green on all the faces and then cut into smaller cubes of sides 2 cm each. Find the number of smaller cubes that have only one face painted.
a68
b96
c78
d49
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Q7
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A cube of side 125 cm is painted red on all the faces and then cut into smaller cubes of sides 25 cm each. Find the number of smaller cubes having at least two faces painted.
a48
b36
c44
d52
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Q8
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A cuboid of length 36 m, breadth 18 m and height 9 m is melted and recast into a cube. Find the length of the diagonal of the cube.
a18√3 m
b15√3 m
c12√3 m
d17√3 m
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Q9
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The areas of three adjacent faces of a cuboidal solid block of wax are 216 cm2, 96 cm2 and 144 cm2. It is melted and 8 cubes of the same size are formed from it. What is the lateral surface area (in cm2) of 3 such cubes?
a648
b432
c576
d288
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Q10
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A cuboid with sides 4, 6 and 8 units is covered with paper. The paper is removed and a square is made from it. What is the side (in units) of the square?
a12.24
b16.62
c14.42
d12.62
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Q11
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The length, breadth and height of a cuboid are in the ratio . The length, breadth and height of the cuboid are increased by and , respectively. Then compared to the original volume, the increase in the volume of the cuboid will be:
a47 times
b26 times
c17 times
d15 times
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Q12
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All the opposite faces of a big cube are coloured with blue, green and black colours. After that is cut into 1331 small equal cubes. How many small cubes are there whose only one face is coloured?
a486
b121
c64
d81
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Q13
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A cuboid of dimensions (6cm × 4cm × 1cm) is painted black on both the surfaces of dimension (4cm × 1cm), green on the surfaces of dimension (6cm × 4cm), and red on the surfaces of dimension (6cm × 1cm). Now the block is divided into various smaller cubes of side 1cm each. The smaller cubes so obtained are separated.If cubes having only black colour are removed, then how many cubes will be left?
a16
b18
c14
d20
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Q14
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Find out the maximum length of a table that can be placed in a room of dimensions 15m by 10 m by 8m.
a18m
b19m
c19.72m
d18.54m
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Q15
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The outer border of a width of 1 cm cube with a side of 5 cm is painted Green on each side, and the remaining space enclosed by this 1 cm path is painted Red. This cube is now cut into 125 smaller cubes, each 1 cm. How many smaller cubes have no painted face is more than smaller cubes having 3 faces painted?
a17
b19
c21
d22
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Q16
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A 6 cm side cube is painted blue on its outer surface and cut into smaller cubes of 1 cm each. How many cubes will have only two faces painted?
a16
b24
c96
d48
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Q17
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Two adjacent faces of a solid cube are painted in white, opposite of this adjacent faces are painted in blue while the remaining faces are painted in red, and then this painted cube is cut into 2744 small cubes. Find out how many cubes have less than two faces painted?
a2498
b2572
c2592
d2484
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Q18
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A cuboid of dimensions (6cm × 4cm × 1cm) is painted black on both the surfaces of dimension (4cm × 1cm), green on the surfaces of dimension (6cm × 4cm), and red on the surfaces of dimension (6cm × 1cm). Now the block is divided into various smaller cubes of side 1cm each. The smaller cubes so obtained are separated. How many cubes will be formed?
a18
b12
c24
d16
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