A circle with a radius of 1/2 ft is dilated by a scale factor of 8. Which statements about the new circle are true? Check all that apply.
A.The length of the new radius will be 4 feet.
B.The length of the new radius will be 32 feet.
C.The new circumference will be 8 times the original circumference.
D.The new circumference will be 64 times the original circumference.
E.The new area will be 8 times the original area.
F. The new area will be 64 times the original area.
G. The new circumference will be 8pi feet.
H. The new area will be 16pi square feet.
he new area will be 16pi square feet.
A C F G H
ACFGH
A C E G
idk but its 2021 wipee
To determine which statements about the new circle are true, we need to use the formula for dilations:
New Length = Scale Factor × Original Length
Let's analyze each statement:
A. The length of the new radius will be 4 feet.
To find the new length of the radius, we can substitute the values into the formula:
New Length = 8 × (1/2) ft = 4 ft
Therefore, this statement is true.
B. The length of the new radius will be 32 feet.
Using the same formula:
New Length = 8 × (1/2) ft = 4 ft
Therefore, this statement is false since the length of the new radius is 4 feet, not 32 feet.
C. The new circumference will be 8 times the original circumference.
The circumference of a circle is given by the formula:
Circumference = 2π × Radius
Using the formula, we can calculate the original circumference:
Original Circumference = 2π × (1/2) ft = π ft
Now, let's calculate the new circumference using the dilated radius:
New Circumference = 2π × 4 ft = 8π ft
Therefore, this statement is true.
D. The new circumference will be 64 times the original circumference.
Since we've already calculated that the new circumference is 8π ft, this statement is false.
E. The new area will be 8 times the original area.
The area of a circle is given by the formula:
Area = π × Radius^2
Using the formula, we can calculate the original area:
Original Area = π × (1/2 ft)^2 = π/4 sq. ft
Now, let's calculate the new area using the dilated radius:
New Area = π × (4 ft)^2 = 16π sq. ft
Therefore, this statement is false since the new area is 16π sq. ft, not 8 times the original area.
F. The new area will be 64 times the original area.
Since we've already calculated that the new area is 16π sq. ft, this statement is false.
G. The new circumference will be 8π feet.
We've already calculated that the new circumference is 8π ft, so this statement is true.
H. The new area will be 16π square feet.
We've already calculated that the new area is 16π sq. ft, so this statement is true.
In summary, the statements that are true are:
A. The length of the new radius will be 4 feet.
C. The new circumference will be 8 times the original circumference.
G. The new circumference will be 8π feet.
H. The new area will be 16π square feet.