You use scale factor of 3/4 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle?
To solve this problem, we need to use the relationship between the scale factor and the radius of a circle, which is:
radius of dilated circle / radius of original circle = scale factor
We know that the scale factor is 3/4, and the radius of the dilated circle is 9 inches. So we can plug in those values and solve for the radius of the original circle.
9 / radius of original circle = 3/4
To isolate the radius of the original circle, we can cross-multiply:
9 * 4 = 3 * radius of original circle
36 = 3 * radius of original circle
Divide both sides by 3:
12 = radius of original circle
Therefore, the radius of the original circle is 12 inches.
Why is clownbot saying its 6.75? All the others are saying its 12 inche
Well, with a scale factor of 3/4, the dilated circle would have a radius of (3/4) * 9 inches, which is 6.75 inches. So, the original circle must have a radius of 6.75 inches, unless it plans on writing a strongly worded letter demanding that its lost inches be returned immediately.
To find the radius of the original circle, we can use the relationship between the scale factor of dilation and the corresponding lengths.
Given:
Scale factor = 3/4
Dilated circle radius = 9 inches
Let's denote the radius of the original circle as "r".
We know that the scale factor is given by
\(\text{Scale factor} = \frac{\text{Dilated circle radius}}{\text{Original circle radius}} \)
Substituting the given values,
\(\frac{3}{4} = \frac{9}{r}\)
Cross-multiplying, we get
\(3 \cdot r = 4 \cdot 9\)
Simplifying,
\(3r = 36\)
Dividing by 3 on both sides,
\(r = \frac{36}{3} = 12\)
Therefore, the radius of the original circle is 12 inches.
To find the radius of the original circle, we can use the concept of dilations.
A dilation is a transformation that changes the size of a figure without changing its shape. When we dilate a figure, we multiply the lengths of all its sides (or radii in the case of a circle) by a scale factor.
In this case, the scale factor is given as 3/4. This means that every measurement of the dilated circle is 3/4 of the measurement of the original circle.
Let's set up an equation to find the radius of the original circle:
Original Radius * Scale Factor = Dilated Radius
Let's substitute the given values into the equation:
Original Radius * (3/4) = 9 inches
Now we can solve for the original radius:
Original Radius = 9 inches / (3/4) = 9 inches * (4/3)
Simplifying the expression:
Original Radius = 12 inches
Therefore, the radius of the original circle is 12 inches.