a circular plate has radius 15cm. every dimension is multiplied by 4 to create a larger, similar plate. how is the ratio of the circumferences related to the ratio of the corresponding dimesions? what is the ratio to the circumferences?(hint: think of circumference as perimeter if a circle.)
All linear dimensions, including the circumference, are multiplied by 4 in the larger plate.
The area is 16 times larger.
To find the ratio of the circumferences of two similar circles, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius.
Let's apply this to the two circular plates. The radius of the original plate is 15 cm, and all dimensions are multiplied by 4 to create a larger, similar plate. Therefore, the radius of the larger plate is 15 cm * 4 = 60 cm.
Now, let's calculate the circumferences of both plates using the formula.
For the original plate:
C1 = 2π * 15 cm
For the larger plate:
C2 = 2π * 60 cm
To find the ratio of the circumferences, we can divide the circumference of the larger plate by the circumference of the original plate:
Ratio of Circumferences = C2 / C1
Substituting the values:
Ratio of Circumferences = (2π * 60 cm) / (2π * 15 cm)
The π (pi) cancels out, leaving us with:
Ratio of Circumferences = 60 cm / 15 cm
Simplifying the ratio gives us the final answer:
Ratio of Circumferences = 4
Therefore, the ratio of the circumferences of the two plates is 4.