A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are Rs. 70. What is the rate of painting per square centimetre?

Options

A. Rs. 0.7
B. Rs. 0.5
C. Rs. 0.1
D. Rs. 0.2

Answer

To find the rate of painting per square centimeter for the wooden box, we will follow these steps:

### Step 1: Calculate the inner dimensions of the box.
The outer dimensions of the box are given as:
- Length = 21 cm
- Width = 11 cm
- Height = 6 cm
- Thickness = 0.5 cm

To find the inner dimensions, we need to subtract the thickness from both sides of the length, width, and height.

**Inner Length** = Outer Length - 2 × Thickness
= 21 cm - 2 × 0.5 cm
= 21 cm - 1 cm
= 20 cm

**Inner Width** = Outer Width - 2 × Thickness
= 11 cm - 2 × 0.5 cm
= 11 cm - 1 cm
= 10 cm

**Inner Height** = Outer Height - Thickness
= 6 cm - 0.5 cm
= 5.5 cm

### Step 2: Calculate the surface area to be painted.
Since the box is open at the top, we will calculate the surface area of the four sides and the bottom.

The formula for the surface area of a cuboid is:
\[ \text{Surface Area} = 2(lb + bh + hl) \]

For our box:
- Length (l) = 20 cm
- Width (b) = 10 cm
- Height (h) = 5.5 cm

The surface area to be painted is:
\[ \text{Surface Area} = l \times h + b \times h + l \times b + l \times b \]
\[ = (20 \times 5.5) + (10 \times 5.5) + (20 \times 10) \]
\[ = 110 + 55 + 200 \]
\[ = 365 \, \text{cm}^2 \]

### Step 3: Calculate the cost of painting per square centimeter.
The total cost of painting is given as Rs. 70.

To find the rate of painting per square centimeter, we use the formula:
\[ \text{Rate per cm}^2 = \frac{\text{Total Cost}}{\text{Surface Area}} \]
\[ = \frac{70}{365} \]

Calculating this gives:
\[ \approx 0.19178 \, \text{Rs/cm}^2 \]

### Step 4: Round the answer.
Rounding this to two decimal places, we get:
\[ \approx 0.19 \, \text{Rs/cm}^2 \]

### Final Answer:
The rate of painting per square centimeter is approximately Rs. 0.19.

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