Question
If the cost of painting 1 cm² is ₹2, what is the cost of painting 12lcm 10wcm 7hcm
a) ₹740 b) ₹760 c) ₹720 d) ₹800
a) ₹740 b) ₹760 c) ₹720 d) ₹800
Answers
GPT-4o mini
To calculate the cost of painting, we first need to find the surface area of the rectangular box with dimensions 12 cm (length), 10 cm (width), and 7 cm (height).
The surface area \( S \) of a rectangular box can be calculated using the formula:
\[
S = 2lw + 2lh + 2wh
\]
Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Substituting the given dimensions:
- \( l = 12 \) cm
- \( w = 10 \) cm
- \( h = 7 \) cm
Now calculating each term:
1. \( 2lw = 2 \times 12 \times 10 = 240 \)
2. \( 2lh = 2 \times 12 \times 7 = 168 \)
3. \( 2wh = 2 \times 10 \times 7 = 140 \)
Now we sum these areas:
\[
S = 240 + 168 + 140 = 548 \text{ cm}^2
\]
Now that we have the surface area, we can calculate the cost of painting:
The cost of painting 1 cm² is ₹2, so for 548 cm², the cost will be:
\[
\text{Cost} = \text{Surface Area} \times \text{Cost per cm²} = 548 \times 2 = ₹1096
\]
However, we notice there are no options close to ₹1096. Let’s double-check our calculations.
1. Calculation of each area term again:
- \( 2lw = 240 \)
- \( 2lh = 168 \)
- \( 2wh = 140 \)
Summing gives \( 240 + 168 + 140 = 548 \).
Now after checking all numbers and multipliers, I realize that the values returned after multiplying may need to be verified against costs typically expected. Potentially an alternate surface area measurement, differing units, or somewhat nullable terms may yield secondary results—but factoring should yield that ₹1096 as a direct paintable area isn't in range.
Would you appreciate verifying these dimensions and potential surface treatments episodically prior to these outputs?
The surface area \( S \) of a rectangular box can be calculated using the formula:
\[
S = 2lw + 2lh + 2wh
\]
Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Substituting the given dimensions:
- \( l = 12 \) cm
- \( w = 10 \) cm
- \( h = 7 \) cm
Now calculating each term:
1. \( 2lw = 2 \times 12 \times 10 = 240 \)
2. \( 2lh = 2 \times 12 \times 7 = 168 \)
3. \( 2wh = 2 \times 10 \times 7 = 140 \)
Now we sum these areas:
\[
S = 240 + 168 + 140 = 548 \text{ cm}^2
\]
Now that we have the surface area, we can calculate the cost of painting:
The cost of painting 1 cm² is ₹2, so for 548 cm², the cost will be:
\[
\text{Cost} = \text{Surface Area} \times \text{Cost per cm²} = 548 \times 2 = ₹1096
\]
However, we notice there are no options close to ₹1096. Let’s double-check our calculations.
1. Calculation of each area term again:
- \( 2lw = 240 \)
- \( 2lh = 168 \)
- \( 2wh = 140 \)
Summing gives \( 240 + 168 + 140 = 548 \).
Now after checking all numbers and multipliers, I realize that the values returned after multiplying may need to be verified against costs typically expected. Potentially an alternate surface area measurement, differing units, or somewhat nullable terms may yield secondary results—but factoring should yield that ₹1096 as a direct paintable area isn't in range.
Would you appreciate verifying these dimensions and potential surface treatments episodically prior to these outputs?