Let's solve each question step by step.
Question 1
A) A circle with a radius of 6 inches is dilated by a scale factor of 4. What is the radius of the transformed circle?
To find the new radius, multiply the original radius by the scale factor: \[ \text{New Radius} = 6 , \text{inches} \times 4 = 24 , \text{inches} \]
Answer: 24 in.
Question 2
A) 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?
The scale factor can be found by dividing the circumference of circle P by the circumference of circle O: \[ \text{Scale Factor} = \frac{\text{Circumference of P}}{\text{Circumference of O}} = \frac{111 , \text{m}}{37 , \text{m}} = 3 \]
Answer: 3 m.
Question 3
A) 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?
First, we find the circumference of circle B using the ratio of the radii. The ratio of the radii is: \[ \text{Scale Factor} = \frac{\text{Radius of B}}{\text{Radius of A}} = \frac{60 , \text{mm}}{6 , \text{mm}} = 10 \] Now, multiply the circumference of circle A by this scale factor: \[ \text{Circumference of B} = 38 , \text{mm} \times 10 = 380 , \text{mm} \]
Answer: 380 mm.
Question 4
A) If circle X is constructed so that it has a circumference of 120 centimeters, and is dilated to create circle X′ with a circumference of 90 centimeters, then what is the scale factor? Enter any non-whole number as a fraction.
The scale factor can be calculated by dividing the circumference of X' by the circumference of X: \[ \text{Scale Factor} = \frac{\text{Circumference of X'}}{\text{Circumference of X}} = \frac{90 , \text{cm}}{120 , \text{cm}} = \frac{3}{4} \]
Answer: \(\frac{3}{4}\) cm.
Question 5
A) If the radius of circle B is 13 feet, and the radius of circle C is 78 feet, then what is the scale factor from circle B to circle C? Enter any non-whole number as a fraction.
The scale factor is found by dividing the radius of circle C by the radius of circle B: \[ \text{Scale Factor} = \frac{\text{Radius of C}}{\text{Radius of B}} = \frac{78 , \text{ft}}{13 , \text{ft}} = 6 \]
Answer: 6 ft.
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