SAT Math Multiple Choice Practice Question 260: Answer and Explanation
A machine uses a laser beam to cut circles from a sheet of plastic, as shown in the figure above. The beam cuts at the rate of 3 cm per second. If circle A has an area of 64π square centimeters and circle B has an area of 16π square centimeters, how many more seconds will it take the machine to cut circle A than circle B?
A. 2π seconds
D. 8π seconds
Correct Answer: B
B To find how many more seconds it will take the machine to cut circle A than circle B, you can find the length of time it takes to cut each circle and subtract them. The laser cuts the circumference of each circle, so you must find that first. Circle A has an area of 64π. Since the area of a circle is . r2, the radius of the circle is 8. Since the area of circle B is 16π, its radius is 4. The circumference of a circle is 22r, so the circumference of A is and the circumference of B is . The difference of their radii is . The time it takes to cut that length is given by the formula time = distance/rate.