A bicycle training wheel has a radius of 3 inches. A regular bicycle wheel has a radius of 10 inches.
Approximately how much smaller, in square inches and rounded to the nearest hundredth, is the area of the training wheel than the area of the regular bicycle wheel?
A. 21.98
B. 153.86
C. 285.74
D. 1,142.96
To calculate the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius.
For the training wheel:
Radius = 3 inches
Area = π(3)^2
Area = π(9)
Area = 9π
For the regular bicycle wheel:
Radius = 10 inches
Area = π(10)^2
Area = π(100)
Area = 100π
Now, let's find the difference in area:
Difference = Area of regular wheel - Area of training wheel
Difference = 100π - 9π
Difference = 91π
To get a numerical value, we can use an approximation for π of 3.14:
Difference ≈ 91 * 3.14
Difference ≈ 285.74
Therefore, the area of the training wheel is approximately 285.74 square inches smaller than the area of the regular bicycle wheel. The answer is C. 285.74.