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0How To Solve Cube And Cuboid Quickly
Surface Area of Cuboid:
- Before delving into the concept of surface areas and volumes of cube and cuboid, it is essential that we learn to make them.
- A cuboid is a three-dimensional representation of a rectangle while a cube is the three-dimensional representation of a square.
- Cuboid is an assemblage of rectangular pieces, similarly, a cube is an assemblage of square shaped pieces as length, breadth, and height.
Surface Area of Cube:
A cube is a 3d representation of a square and has all equal sides. The length, breadth, and height in a cube are the same and are termed as sides (s). If s is each edge of the cube then, the surface area of a cube:
- 2 [(s × s) + (s × s) + (s × s)] = 2 ( 3s2) = 6s2
How To Solve Cube and Cuboid Questions Quickly:
The following questions are based on the information given below:
- There is a cuboid whose dimensions are 4 x 3 x 3 cm.
- The opposite faces of dimensions 4 x 3 are coloured yellow.
- The opposite faces of other dimensions 4 x 3 are coloured red.
- The opposite faces of dimensions 3 x 3 are coloured green.
- Now the cuboid is cut into small cubes of side 1 cm.
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Question 1) A 2 inch cube (2 x 2 x 2) of silver weighs 1.5 kilos and is worth Rs1000.how much is a three inch cube of silver worth ?
(A) 1875
(B) 3375
(C) 2250
(D) 2800
Answer: Option B
Explanation: 8 inch cube = Rs 1000
1 inch cube = \frac{Rs 1000}{8} = Rs 125
27 inch cube = Rs 125\times 27 = Rs 3375
Question 2) All faces of a cube with an eight – meter edge are painted red. If the cube is cut into smaller cubes with a two – meter edge, how many of the two meter cubes have paint on exactly one face?
(A) 24
(B) 36
(C) 60
(D) 48
Answer: Option A
Explanation: If there are n cubes lie on an edge, then total number of cubes with one side painting is given by 6×(n−2)2. Here side of the bigger cube is 8, and small cube is 2. So there are 4 cubes lie on an edge. Hence answer = 24.
How To Solve Cube and Cuboid Questions Quickly:
The following questions are based on the information given below:
There is a cuboid whose dimensions are 4 x 3 x 3 cm.The opposite faces of dimensions 4 x 3 are coloured yellow.The opposite faces of other dimensions 4 x 3 are coloured red.The opposite faces of dimensions 3 x 3 are coloured green.Now the cuboid is cut into small cubes of side 1 cm.
Question 3) How many small cubes will have only two faces colored?
(A) 12
(B) 24
(C) 13
Answer: Option D
Explanation:
Number of small cubes having only two faces coloured = 6 from the front + 6 from the back + 2 from the left + 2 from the right
= 16
Question 4 ) How many small cubes will have only one face coloured ?
(A) 10
(B) 12
(C) 14
(D) 18
Answer: Option A
Explanation: Number of small cubes having only one face coloured = 2 x 2 + 2 x 2 + 2 x 1
= 4 + 4 + 2
= 10
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