A ball rolls along a circle whose radius is 2 ft. How far does the ball roll if it goes around the circle 12.5 times?
I got 25 ft as my answer. I just multiplied the two numbers and I got 25. Is this right?
Nope. The distance around the circle is PI*4.
PI*4*12.5= ? way over 25. Way over 100, but not over 200
Oops. I assume the ball is rolling around the circumference of the circle, not the radius.
To find the circumference of the circle, use this formula, in which C = circumference, r = radius, and pi - 3.14
C = 2r * pi
C = 4 * 3.14
C = ?
Now multiply 12.5 by the circumference.
If you post your answer we'll check it. You can also study about the circumference at this site.
http://www.mathgoodies.com/lessons/vol2/circumference.html
is it 157.1?
I got 157 feet.
how did you get that?
Using Bobpursley's formula of PI*4*12.5 =
3.14 * 4 * 12.5 = 157
No, multiplying the radius and the number of times the ball goes around the circle will not give you the correct answer. To find the distance the ball rolls, you need to calculate the circumference of the circle and then multiply it by the number of times the ball goes around.
To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, the radius is 2 ft. So, the circumference of the circle is:
C = 2π(2) = 4π ft
Then, you multiply the circumference by the number of times the ball goes around the circle, which is 12.5:
Distance = 4π ft x 12.5 = 50π ft
Using an approximate value for π (3.14159), the distance the ball rolls is approximately:
Distance ≈ 50(3.14159) ≈ 157.08 ft
Therefore, the ball rolls approximately 157.08 ft, not 25 ft.