A large ice cube is melting at a rate of cm³ per minute, where t is time in minutes. If is the volume of the ice cube at time t = 0 minutes, which one of the following expresses the volume of the ice cube after 4 hours?

Question

Quizplus · Accepted Answer

We can use the formula for the volume of a cube:

V = s^3

where s is the side length of the cube.

Let V0 be the initial volume of the cube, and let t be the time in minutes. We are told that the rate of melting is:

s'/dt = -11eb69ff_febf_783d_af94_0701c7d9048f_TB8190_11

where s' is the rate of change of the side length. We can use the chain rule to write:

dV/dt = 3s^2 ds/dt

Substituting s = (V/3)^(1/3), and using the given rate of melting, we get:

dV/dt = -11eb69ff_febf_783d_af94_0701c7d9048f_TB8190_11 V^(2/3)

This is a separable differential equation that can be solved using integration. We get:

V^(1/3) = [V0^(1/3) - (11eb69ff_febf_783d_af94_0701c7d9048f_TB8190_11/3) t]^[3/2]

At t = 4 hours = 240 minutes, we have:

V = [V0^(1/3) - (11eb69ff_febf_783d_af94_0701c7d9048f_TB8190_11/3) (240)]^3

Simplifying:

V = (V0 + 11eb69ff_febf_9f50_af94_fb8049f1c1eb_TB8190_11)^3

Therefore, the answer is B, 11eb69ff_febf_9f50_af94_fb8049f1c1eb_TB8190_11.

A Large Ice Cube Is Melting at a Rate of