Question

A circle with a radius of 1/2ft is dilated by a scale factor of 8. Which statements about the new circle are true? Check all that apply. The length of the new radius will be 4 feet. The length of the new radius will be 32 feet. The new circumference will be 8 times the original circumference. The new circumference will be 64 times the original circumference. The new area will be 8 times the original area. The new area will be 64 times the original area. The new circumference will be feet. The new area will be square feet.

Answer 1

Answer:

A,C,F,G,H

Step-by-step explanation:

According to the given statement the radius of the circle before dilation is 1/2ft and the scale factor is 8. The dilation by scale factor 8 means the radius of new circle is 8 times of the original circle(4ft)

The circumference of the circle is 2πr.

If we replace r by 8r and substitute it in the formula then the circumference will be:

C=2π(8r)

C=8*(2πr)

It means the circumference is 8 times the original circumference.

Now put the value of original circle radius in this new circumference we get:

C=8*(2πr)

C=8*(2π*1/2)

C=8πft

Now the area of the circle = πr^2

Now put the value of r replaced by 8r in the formula.

A=π(8r)^2

A=64πr^2

Thus the area will be 64 times by the original circle area

If we plug the value of original circle radius in this new formula of area we get.

A=64πr^2

A=64π(1/2)^2

A= 16πft^2

Thus the correct statements are: A, C, F,G,H....