Consider the circles shown. Circle A has a radius of 6 inches. Circle B has a radius 20% greater than Circle A.
The figure shows two circles labeled as Upper A and Upper B of different radii. The diameter of the circle Upper A is labeled as 6 centimeters.
Which area is greater than or equal to the area of Circle B? Select all that apply.
A.
189.31 square inches
B.
51.84 square inches
C.
113.04 square inches
D.
162.78 square inches
E.
203.15 square inches
F.
148.49 square inches
oof i need an answer for this too lmao
Right answers A,D,E
trust me ^-^
for connexus students
so wht
To solve this problem, we need to find the areas of both Circle A and Circle B and compare them.
1. Circle A has a radius of 6 inches. The area of a circle is calculated using the formula A = πr^2, where r is the radius.
Substituting the given value, we get A_A = π(6^2) = 36π square inches.
2. Circle B has a radius 20% greater than Circle A. To find the radius of Circle B, we need to calculate 20% of the radius of Circle A and add it to the radius of Circle A.
20% of 6 inches = (20/100) * 6 = 1.2 inches. Adding this to the radius of Circle A:
Radius of Circle B = 6 inches + 1.2 inches = 7.2 inches.
Calculating the area of Circle B using the formula A = πr^2:
A_B = π(7.2^2) = 51.84π square inches.
Now, we need to compare the areas and identify which options are greater than or equal to the area of Circle B.
Calculating the approximate values of the areas:
A_A ≈ 36(3.14) ≈ 113.04 square inches
A_B ≈ 51.84(3.14) ≈ 162.78 square inches
Based on the calculations, the area of Circle A is approximately 113.04 square inches, and the area of Circle B is approximately 162.78 square inches.
Therefore, the answer options that are greater than or equal to the area of Circle B are:
A. 189.31 square inches
D. 162.78 square inches
E. 203.15 square inches
F. 148.49 square inches