please help asap

Question

A spherical balloon is being inflated by a compressor that is pumping air at a rate of  At 4.9ft^3 /min . what rate is the radius of the balloon increasing when the radius is 1.5 ft  Round to three decimal places.

Answer 1

V = (4/3) PI * R^3

dV/dt = 4 PI R^2 * dR/dt

4.9 = 4 * pi * (1.5)^2 * dr/dt

4.9 / [ 4 * pi * 1/.5^2] = dr/dt

Answer 2

Let the rate that the volume increases/decreases be represented by:

dV/dt = 4.9

Your goal is to solve for dr/dt (the rate at which the radius is increasing/decreasing).

Start with the general formula for the volume of a sphere:

V = (4/3)π r ³

Differentiate both sides with respect to t (time).

dV/dt = 4π r ²(dr/dt)

Plug in the information provided in the question, dV/dt = 4.9 and r = 1.5.

4.9 = 4π (1.5)² (dr/dt)

Solve for the expression dr/dt, which represents the rate the radius is changing.

Ask me if you are unsure about anything in this explanation.