The amount of paint needed is directly proportional to the circumference of the track. The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius. We can use this formula to find the ratio of the circumference of the two tracks:
C1/C2 = (2πr1)/(2πr2) = r1/r2
where C1 is the circumference of the first track (with radius r1) and C2 is the circumference of the second track (with radius r2).
We know that it takes 103 gallons of paint to paint the first track, so let's call the amount of paint needed for the second track P2. We can set up a ratio of the paint amounts:
103/P2 = C1/C2 = r1/r2
Substituting r1 = 1/4 mile and r2 = 1/5 mile:
103/P2 = (1/4)/(1/5) = 5/4
Multiplying both sides by P2:
P2 = 103 × 4/5 = 82.4
Therefore, it would take approximately 82.4 gallons of paint to paint a center stripe around a circular track that has a radius of one-fifth of a mile.
If it takes one hundred three gallons of paint to paint a center stripe around a circular track that has a radius of one-fourth of a mile, then how much paint would it take to paint a center stripe around a circular track that had a radius of one-fifth of a mile?
1 answer