Question
Elspeth knows that Pi times r almost-equals 9.42 centimeters. What would she need to do to find the circumference?
She could multiply 9.42 by 2.
She could multiply 9.42 by Pi.
She could divide 9.42 by 2 to find the radius, and then square the radius.
She could divide 9.42 by Pi to find the radius, and then multiply 9.42 by the radius.
She could multiply 9.42 by 2.
She could multiply 9.42 by Pi.
She could divide 9.42 by 2 to find the radius, and then square the radius.
She could divide 9.42 by Pi to find the radius, and then multiply 9.42 by the radius.
Answers
Answered by
GPT-4o mini
To find the circumference using the relationship given (Pi times r ≈ 9.42 centimeters), Elspeth can use the following approach:
She knows that the formula for the circumference (C) of a circle is:
\[ C = 2 \times \pi \times r \]
From the information given, we have:
\[ \pi \times r \approx 9.42 \]
To find the circumference (C), she can manipulate the formula. Firstly, she can isolate \( r \):
1. Divide both sides of the initial equation by \( \pi \) to find \( r \):
\[ r \approx \frac{9.42}{\pi} \]
2. Next, to find the circumference, substitute \( r \) back into the circumference formula:
\[ C \approx 2 \times \pi \times \left(\frac{9.42}{\pi}\right) \]
This simplifies to:
\[ C \approx 2 \times 9.42 = 18.84 \text{ centimeters} \]
However, the option listed that directly relates to finding the circumference from the given information is:
**She could multiply 9.42 by Pi.**
This option effectively calculates the circumference (C), but it's worth noting that the full direct relationship requires multiplying \( 2 \) as well if you want the complete circumference.
In summary, while simply multiplying 9.42 by Pi would give you a value related to it (as part of the circumference formulas), properly to find the complete circumference, you should multiply by \( 2 \) after dividing to isolate \( r \). The accurate step given the context would indeed be to multiply it by Pi, but make sure to include \( 2r \) for completeness. The intention here should reflect checking through the options' intended meanings and steps to yield \( C \).
She knows that the formula for the circumference (C) of a circle is:
\[ C = 2 \times \pi \times r \]
From the information given, we have:
\[ \pi \times r \approx 9.42 \]
To find the circumference (C), she can manipulate the formula. Firstly, she can isolate \( r \):
1. Divide both sides of the initial equation by \( \pi \) to find \( r \):
\[ r \approx \frac{9.42}{\pi} \]
2. Next, to find the circumference, substitute \( r \) back into the circumference formula:
\[ C \approx 2 \times \pi \times \left(\frac{9.42}{\pi}\right) \]
This simplifies to:
\[ C \approx 2 \times 9.42 = 18.84 \text{ centimeters} \]
However, the option listed that directly relates to finding the circumference from the given information is:
**She could multiply 9.42 by Pi.**
This option effectively calculates the circumference (C), but it's worth noting that the full direct relationship requires multiplying \( 2 \) as well if you want the complete circumference.
In summary, while simply multiplying 9.42 by Pi would give you a value related to it (as part of the circumference formulas), properly to find the complete circumference, you should multiply by \( 2 \) after dividing to isolate \( r \). The accurate step given the context would indeed be to multiply it by Pi, but make sure to include \( 2r \) for completeness. The intention here should reflect checking through the options' intended meanings and steps to yield \( C \).