Question
A circle with a radius of 6 inches is dilated by a scale factor of 4. What is the radius of the transformed circle?
Answers
Answer
If circle O
has a circumference of 37 meters and circle P
has a circumference of 111 meters, then what is the scale factor from O
to P
?
has a circumference of 37 meters and circle P
has a circumference of 111 meters, then what is the scale factor from O
to P
?
Answer
If circle A
has a radius of 6 millimeters, with a circumference of approximately 38 millimeters, and circle B
has a radius of 60 millimeters, then what is circle B
’s approximate circumference?
has a radius of 6 millimeters, with a circumference of approximately 38 millimeters, and circle B
has a radius of 60 millimeters, then what is circle B
’s approximate circumference?
Answered by
GPT 3.5
To find the radius of the transformed circle, we multiply the original radius by the scale factor.
Original radius: 6 inches
Scale factor: 4
Transformed radius = Original radius x Scale factor
Transformed radius = 6 x 4
Transformed radius = 24
Therefore, the radius of the transformed circle is 24 inches.
Original radius: 6 inches
Scale factor: 4
Transformed radius = Original radius x Scale factor
Transformed radius = 6 x 4
Transformed radius = 24
Therefore, the radius of the transformed circle is 24 inches.
Answered by
GPT 3.5
The scale factor between two circles is the ratio of their circumferences.
Let's denote the scale factor as \( k \). Given that circle O has a circumference of 37 meters and circle P has a circumference of 111 meters, we can set up the following equation:
\[ k = \frac{\text{Circumference of P}}{\text{Circumference of O}} \]
\[ k = \frac{111}{37} \]
\[ k = 3 \]
Therefore, the scale factor from circle O to circle P is 3.
Let's denote the scale factor as \( k \). Given that circle O has a circumference of 37 meters and circle P has a circumference of 111 meters, we can set up the following equation:
\[ k = \frac{\text{Circumference of P}}{\text{Circumference of O}} \]
\[ k = \frac{111}{37} \]
\[ k = 3 \]
Therefore, the scale factor from circle O to circle P is 3.
Answered by
GPT 3.5
To find the circumference of circle B with a radius of 60 millimeters, we can use the formula for the circumference of a circle:
\[ \text{Circumference} = 2 \times \pi \times \text{radius} \]
Given that circle A has a radius of 6 millimeters and a circumference of 38 millimeters, we can find the value of π (Pi) using the relationship between the radius and circumference:
\[ \text{Circumference of A} = 2 \times \pi \times \text{radius of A} \]
\[ 38 = 2 \times \pi \times 6 \]
\[ 38 = 12\pi \]
\[ \pi ≈ \frac{38}{12} ≈ 3.17 \]
Now, we can find the circumference of circle B with a radius of 60 millimeters using the calculated value of π:
\[ \text{Circumference of B} = 2 \times 3.17 \times 60 \]
\[ \text{Circumference of B} ≈ 2 \times 3.17 \times 60 \]
\[ \text{Circumference of B} ≈ 377.4 \text{ millimeters} \]
Therefore, the approximate circumference of circle B with a radius of 60 millimeters is approximately 377.4 millimeters.
\[ \text{Circumference} = 2 \times \pi \times \text{radius} \]
Given that circle A has a radius of 6 millimeters and a circumference of 38 millimeters, we can find the value of π (Pi) using the relationship between the radius and circumference:
\[ \text{Circumference of A} = 2 \times \pi \times \text{radius of A} \]
\[ 38 = 2 \times \pi \times 6 \]
\[ 38 = 12\pi \]
\[ \pi ≈ \frac{38}{12} ≈ 3.17 \]
Now, we can find the circumference of circle B with a radius of 60 millimeters using the calculated value of π:
\[ \text{Circumference of B} = 2 \times 3.17 \times 60 \]
\[ \text{Circumference of B} ≈ 2 \times 3.17 \times 60 \]
\[ \text{Circumference of B} ≈ 377.4 \text{ millimeters} \]
Therefore, the approximate circumference of circle B with a radius of 60 millimeters is approximately 377.4 millimeters.
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