The edges of a cube increase at a rate of 2 cm/s. How fast is ...

Question

The edges of a cube increase at a rate of 2 cm/s. How fast is the volume changing when the length of each edge is 50 cm?

Accepted Answer

Welcome back, everyone. The radius of a circular pond is expanding at a rate of 0.5 m per second. Determine the rate at which the area of the pond is increasing when the radius is 20 m. A says it's 40 square meters per second. B 100 square meters per second, C 30 square meters per second, and D 20 square meters per second. Now how are we going to find the rate at which the area of the pond is increasing? What do we know about the area? Well, since it's a circular pond, OK, then recall that the area of a circle. Is equal to pi R squared. So to find the rate at which the area is increasing, we're going to differentiate a differentiate our formula, OK. With risk, let me write out the formula here. We're going to differentiate it with respect to tea because we're talking about the rate at which the area is increasing. And now when we do that. Then the derivative of A with respect to T is going to be equal to 2 piR multiplied by DRDT, the rate at which the radius is increasing. Now we know that we're looking for the rate when the radius is 20 m. OK, so in this case, R equals 20 m. And we also know that our problem told us the radius is expanding at a rate of 0.5 m per second. So in other words, the rate. Sorry, the derivative of R with respect to T will be equal to 0.5. So since we have these values, if we substitute them into our equation for the derivative of the area with respect to time, that means it will be equal to 2 multiplied by 20 m, multiplied by 0.5 m per second. Which is going to be equal to 25 square meters per second. Thus, the area is increasing at a rate of 20 square meters per second when the radius is 20 m. Therefore, D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

The edges of a cube increase at a rate of 2 cm/s. How fast is the volume changing when the length of each edge is 50 cm?

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