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# How To Solve Cube And Cuboid Quickly

## How To Solve Cube And Cuboid Questions Quickly

**Cuboid and Cube have the basic formulas to understand and learn for the exact solutions of the questions . One has to be very precise and have clear concept of cuboid and cube to learn and analyse the basic details of the problems .**

## 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 ( 3s
^{2}) = 6s^{2}

## 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 1) A 2 inch cube (2*2*2) of silver weighs 1.5 kilos and is worth Rs1000.how much is a three inch cube of silver worth ?**

(A) 18750

(B) 33750

(C) 22500

(D) 28000

**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?**

#### Answer: Option C

#### 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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