Cubes and Cuboids
18 solved SSC CGL Quantitative Aptitude previous year questions on Cubes and Cuboids, each with the correct answer and a full explanation.
Q1
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?
✓ 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
How many cubes of 2 cm can be cut out of a cube of 12 cm length?
✓ 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
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.
✓ Correct answer: d) 150
ExplanationGiven, Cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides 7 cm each n = 49/7 = 7 Number of cubes one side painted = 6 (n-2)2 Number of cubes one side painted = 6 (7-2)2 = 6 × 25 = 150 Hence, 150 is the correct answer.
Q4
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.
✓ Correct answer: b) 48
ExplanationGiven that: side (n) = 18 n = 18/3 = 6 So, two faces painted cubes = 12(n-2) 12 x 4 = 48 Hence, 48 is the correct answer.
Q5
The surface area of a cube is 864 . The volume of the cube is _______.
✓ Correct answer: a) 1728
ExplanationLet the edge of cube = P cm So, Surface area of cube = 864 Hence required volume of cube = 1728 cm3 Hence, the correct answer is (A).
Q6
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.
✓ Correct answer: b) 96
ExplanationThe number of cubes is more in question, but it has to be shaded like this: Cubes that have only one face painted = n = = 6 Putting value in the formula, we got: So, 16 × 6 = 96 Hence, 96 is the correct answer.
Q7
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.
✓ Correct answer: c) 44
ExplanationHere, n = = 5 No. of cubes with 2 sides painted = 12(n – 2) = 12 (5 – 2) = 12 × 3 = 36 No. of cubes with 3 sides painted = 8 36 + 8 = 44 total such cubes with at least 2 sides painted.Hence, Option C is the correct answer.
Q8
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.
✓ Correct answer: a) 18√3 m
ExplanationLength of cuboid = 36 m Breadth of cuboid = 18 m Height of cuboid = 9 m Volume of cube =Volume of Cuboid The diagonal of cube m Hence, Option A is the correct answer.
Q9
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?
✓ Correct answer: b) 432
ExplanationLet sides of cuboid be a, b and c According to question, ab = 216 ……(1) bc = 96 ……(2) ca = 144 ……(3) Multiplying all three equations ab × bc × ca = 216 × 96 × 144 (abc)2 = 36 × 6 × 6 × 16 × 144 abc = 6 × 6 × 4 × 12 = 1728 Let the side of 8 cubes be y 8 × y3 = 1728 y3 = 216 y = 6 Required Lateral surface area of 3 such cubes = 3 × 4y2 = 3 × 4 × 62 = 432 Hence, 432 is the correct answer.
Q10
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?
✓ Correct answer: c) 14.42
ExplanationA cuboid has 6 faces, and each face is a rectangle.The formula for the surface area of a cuboid is: Surface Area = 2(lw + lh + wh) So, the total surface area of the cuboid is 208 square units.Now, when you remove the paper and make a square from it, the area of the square will be equal to the total surface area of the cuboid.Therefore, the side length (s) of the square can be found by taking the square root of the total surface area: s = √208≈ 14.42 units So, the side length of the square that can be made from the paper that covered the cuboid is approximately 14.42 units.Hence, option C is correct
Q11
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:
✓ Correct answer: a) 47 times
ExplanationLet, length of cuboid = a unit Let, breadth of cuboid = 2a unit Let, height of cuboid = 3a unit Original volume of cuboid cube unit Length of cuboid after 200% increase unit Breadth of cuboid after 300% increase unit Height of cuboid after 300% increase unit Increased volume of cuboid cube unit Increase in volume cube unit original volume Hence, the correct answer is (A).
Q12
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?
✓ Correct answer: a) 486
ExplanationHere, in the given question, we have to find out how many small cubes there are whose only one face is coloured.Total number of small cubes having only one face coloured = 6(n - 2)2 Here, n = = 6(11 - 2)2 = 6 × 81 = 486 So, 486 cubes have only one face coloured.Hence, 486 is the correct answer.
Q13
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?
✓ Correct answer: a) 16
ExplanationHere, in the given question we have to find out If cubes having only black colour are removed, then how many cubes will be left.According to the given information, we get the following figure: So, the total number of cubes is 16 that are left after removing black-coloured cubes.Hence, 16 is the correct answer.
Q14
Find out the maximum length of a table that can be placed in a room of dimensions 15m by 10 m by 8m.
✓ Correct answer: c) 19.72m
ExplanationHere, in the given question we have to find out the maximum length of a table that can be placed in a room.The maximum length of the bed is the diagonal of the room.Diagonal of cuboid = So, the maximum length of a bed that can be placed in a room is 19.72m.Hence, 19.72m is the correct answer.
Q15
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?
✓ Correct answer: b) 19
ExplanationHere, in the given question, we have to find out how many smaller cubes have no painted face is more than smaller cubes having 3 faces painted.According to the given information, we get this figure: Now, n3 = 125 n = 5 Total number of cubes having no paint = (n - 2)3 = (5 - 2)3 = 27 Total number of cubes having 3 faces painted = 8 So, the smaller cubes have no painted face is more than smaller cubes having 3 faces painted = 27 - 8 = 19 Hence, 19 is the correct answer.
Q16
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?
✓ Correct answer: d) 48
ExplanationAs per the figure shown below the cubes having only two faces coloured will be: The number of smaller cubes with two surface painted = (n−2) 12 As (n) = , here (n) = 6, and the total number of edges in a cube = 12 So, two side painted = (6−2) 12 = 4 12 = 48 Hence, the correct answer is 48.
Q17
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?
✓ Correct answer: c) 2592
ExplanationHere, in the given question we have to find out the total cubes that have one or no face painted.Now, n3 = 2744 n = 14 The total number of cubes have one side painted: 6 (n - 2)2 = 6 (14 - 2)2 = 864 The total number of cubes that have no face painted: (n - 2)3 = (14 - 2)3 = 1728 So, the total cubes that have less than one face painted is 864 + 1728 = 2592 Hence, 2592 is the correct answer.
Q18
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?
✓ Correct answer: c) 24
ExplanationHere, in the given question we have to find out how many cubes will be formed.According to the given information, we get the following figure: So, the total number of cubes formed is (6 × 4) = 24 cubes.Hence, 24 is the correct answer,
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