Answer :
To solve this problem, we need to determine the remaining area of the cardboard after two circles have been punched out of it.
1. Step 1: Understand the given data:
- The area of the rectangular piece of cardboard is 258 cm².
- The multiple-choice answers for the remaining area after punching out two circles are given as 227 cm², 246 cm², and 258 cm².
2. Step 2: Determine which of the given areas correspond to the remaining cardboard after the circles have been removed:
- Subtract the remaining area from the rectangle area to find the area of the circles.
3. Step 3: Calculate the area of the circles punched out:
- When the remaining cardboard area is 227 cm², the area of the circles punched out is:
[tex]\[ \text{Area of circles} = 258 \, \text{cm}^2 - 227 \, \text{cm}^2 = 31 \, \text{cm}^2 \][/tex]
- When the remaining cardboard area is 246 cm², the area of the circles punched out is:
[tex]\[ \text{Area of circles} = 258 \, \text{cm}^2 - 246 \, \text{cm}^2 = 12 \, \text{cm}^2 \][/tex]
4. Step 4: Determine the accuracy of areas:
- If the calculation involves two circles with areas 31 cm² and 12 cm² respectively, then the remaining area of 227 cm² and 246 cm² from other choices are not valid together in this context only.
5. Conclusion:
- After carefully examining the steps, the most accurate solution shed a unique perspective toward option’s credibility overall.
Since the remaining areas after punching out two circles are computed correctly to be 227 cm² and 246 cm² with areas of circles being correct too.
Therefore, the area remaining is
\[
227 \text {cm}^2
246 \text {cm}^2
]
1. Step 1: Understand the given data:
- The area of the rectangular piece of cardboard is 258 cm².
- The multiple-choice answers for the remaining area after punching out two circles are given as 227 cm², 246 cm², and 258 cm².
2. Step 2: Determine which of the given areas correspond to the remaining cardboard after the circles have been removed:
- Subtract the remaining area from the rectangle area to find the area of the circles.
3. Step 3: Calculate the area of the circles punched out:
- When the remaining cardboard area is 227 cm², the area of the circles punched out is:
[tex]\[ \text{Area of circles} = 258 \, \text{cm}^2 - 227 \, \text{cm}^2 = 31 \, \text{cm}^2 \][/tex]
- When the remaining cardboard area is 246 cm², the area of the circles punched out is:
[tex]\[ \text{Area of circles} = 258 \, \text{cm}^2 - 246 \, \text{cm}^2 = 12 \, \text{cm}^2 \][/tex]
4. Step 4: Determine the accuracy of areas:
- If the calculation involves two circles with areas 31 cm² and 12 cm² respectively, then the remaining area of 227 cm² and 246 cm² from other choices are not valid together in this context only.
5. Conclusion:
- After carefully examining the steps, the most accurate solution shed a unique perspective toward option’s credibility overall.
Since the remaining areas after punching out two circles are computed correctly to be 227 cm² and 246 cm² with areas of circles being correct too.
Therefore, the area remaining is
\[
227 \text {cm}^2
246 \text {cm}^2
]
