Question

Paul is making a ball-toss game for his club booth at the fair. He wants to make the circumference of the holes at least 3 inches greater but not more than 4 inches greater than the circumference of the ball. One person suggests that Paul can make the diameter of the hole 1 inch greater than that of the ball. Another suggests the diameter should be 2inches greater. Which suggestion should Paul choose? Explain

Answer 1

Paul can make the diameter of the hole 1 inch greater than that of the ball

Explanation:

we are going to assume a diameter of the hole has 6in

the radius of the ball is 3in

we looking at a range of the hole greater by (3<4)

we know that the circumference of a circle is given as

the circumference of the ball is

C=2πr

C=2*3.142*3

C=18.85in

The circumference of the hole is ( 1 inch greater )

C=2πr

say the diameter is 6in plus 1in = 7in

the radius =3.5in

C=2*3.142*3.5

C=21.99

compare with the ball the difference is 21.99-18.85

=3.14 which is in the range

The circumference of the hole is ( 2inches greater. )

C=2πr

say the diameter is 6in plus 2in = 8in

the radius =4in

C=2*3.142*4

C=25.13in

compare with the ball the difference is 25.13-18.85

=6.28 which is out of the range