The side length of a square is increasing at a rate of 15 millimeters per second.At a certain instant, the side length is 22 millimeters.What is the rate of change of the area of the square at that instant (in square millimeters per second)?Choose 1 answer:(A) 225(B) 660(C) 484(D) 30
Q. The side length of a square is increasing at a rate of 15 millimeters per second.At a certain instant, the side length is 22 millimeters.What is the rate of change of the area of the square at that instant (in square millimeters per second)?Choose 1 answer:(A) 225(B) 660(C) 484(D) 30
Area Formula: The area of a square is given by the formula Area=side length×side length. Let's denote the side length as 's'. So, Area=s2.
Differentiation with Respect to Time: To find the rate of change of the area, we need to differentiate the area with respect to time t. So we get dtd(Area)=2×s×dtds.
Given Values: We know that dtds (the rate of change of the side length) is 15mm/s and at the instant we are considering, s=22mm.
Calculation: Now we plug in the values: dtd(Area)=2×22mm×15mm/s=2×330mm2/s=660mm2/s.
Final Answer: So, the rate of change of the area of the square at that instant is 660 square millimeters per second. The correct answer is (B) 660.
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