Question
If the cost of painting 1 cm² is ₹2, what is the cost of painting 12lcm 10wcm 7hcm
Answers
GPT-4o mini
To find the cost of painting the surface of a rectangular box with dimensions of 12 cm (length), 10 cm (width), and 7 cm (height), we need to calculate the surface area of the box first.
The surface area \( A \) of a rectangular box can be calculated using the formula:
\[
A = 2lw + 2lh + 2wh
\]
Where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Substituting the given values:
- \( l = 12 \) cm
- \( w = 10 \) cm
- \( h = 7 \) cm
Now, we calculate each term:
1. \( 2lw = 2 \times 12 \times 10 = 240 \, \text{cm}^2 \)
2. \( 2lh = 2 \times 12 \times 7 = 168 \, \text{cm}^2 \)
3. \( 2wh = 2 \times 10 \times 7 = 140 \, \text{cm}^2 \)
Now, summing these areas:
\[
A = 240 + 168 + 140 = 548 \, \text{cm}^2
\]
Now, to find the cost of painting the surface, we multiply the surface area by the cost per cm²:
\[
\text{Cost} = \text{Area} \times \text{Cost per cm}^2 = 548 \times 2 = ₹1096
\]
Therefore, the cost of painting the box is ₹1096.
The surface area \( A \) of a rectangular box can be calculated using the formula:
\[
A = 2lw + 2lh + 2wh
\]
Where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Substituting the given values:
- \( l = 12 \) cm
- \( w = 10 \) cm
- \( h = 7 \) cm
Now, we calculate each term:
1. \( 2lw = 2 \times 12 \times 10 = 240 \, \text{cm}^2 \)
2. \( 2lh = 2 \times 12 \times 7 = 168 \, \text{cm}^2 \)
3. \( 2wh = 2 \times 10 \times 7 = 140 \, \text{cm}^2 \)
Now, summing these areas:
\[
A = 240 + 168 + 140 = 548 \, \text{cm}^2
\]
Now, to find the cost of painting the surface, we multiply the surface area by the cost per cm²:
\[
\text{Cost} = \text{Area} \times \text{Cost per cm}^2 = 548 \times 2 = ₹1096
\]
Therefore, the cost of painting the box is ₹1096.