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Mathematics (09) Practice TestSECOND SAMPLE WEAK RESPONSE FOR OPEN-RESPONSEITEM ASSIGNMENT #2In analyzing the rubber ball making machine, the rubber stock fed is 1" in diameter. This stock fedis what the balls are being made out of. This in turn makes the rubber balls with a diameter of oneinch.Volume of rubber ballSince the ball is a sphere, V = 4 3 πr 3Since the diameter = 1", r = 0.5"Therefore, V = 4 3 π • 0.5 3 = 4 3π • 0.125 = 0.523 cubic inchesVolume of rubber stockSince the stock is a cylinder, V = πr 2 hSince the diameter = 1", r = 0.5"Since the piece of stock is one foot long, h = 12"Therefore, V = 3.14 • 0.5 2 • 12 = 3.14 • 0.25 • 12 = 9.42 cubic inchesS(d)S = speed = 3 balls per secondd = diameter = 1 inchTherefore, S(d) = 3 • 1 = 3Graph of S(d) for values of d from 0.5" to 2.5"3(0.5) = 1.53(1) = 33(1.5) = 4.53(2) = 63(2.5) = 7.591