The volume V of a right circular cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Given that the radius r is increasing at a rate of 0.2 cm/sec (dr/dt = 0.2) and the height h is decreasing at a rate of 0.1 cm/sec (dh/dt = -0.1), we want to find the rate of change of the volume dV/dt when r = 1 cm and h = 2 cm.

We can find this by differentiating the volume formula with respect to time t, using the chain rule:

dV/dt = π * (2rh * dr/dt + r² * dh/dt)

Substituting the given values:

dV/dt = π * (2 * 1cm * 2cm * 0.2 cm/sec - 1cm² * 0.1 cm/sec)
= π * (0.8 cm³/sec - 0.01 cm³/sec)
= π * 0.79 cm³/sec

So, the rate of change of the volume of the cylinder is approximately 0.79π cm³/sec.

Question

The volume V of a right circular cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Given that the radius r is increasing at a rate of 0.2 cm/sec (dr/dt = 0.2) and the height h is decreasing at a rate of 0.1 cm/sec (dh/dt = -0.1), we want to find the rate of change of the volume dV/dt when r = 1 cm and h = 2 cm.

We can find this by differentiating the volume formula with respect to time t, using the chain rule:

dV/dt = π * (2rh * dr/dt + r² * dh/dt)

Substituting the given values:

dV/dt = π * (2 * 1cm * 2cm * 0.2 cm/sec - 1cm² * 0.1 cm/sec)
       = π * (0.8 cm³/sec - 0.01 cm³/sec)
       = π * 0.79 cm³/sec

So, the rate of change of the volume of the cylinder is approximately 0.79π cm³/sec.

Knowee AI · Accepted Answer

The volume V of a right circular cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Given that the radius r is increasing at a rate of 0.2 cm/sec (dr/dt = 0.2) and the height h is decreasing at a rate of 0.1 cm/sec (dh/dt = -0.1), we want to find the rate of change of the volume dV/dt when r = 1 cm and h = 2 cm.

We can find this by differentiating the volume formula with respect to time t, using the chain rule:

dV/dt = π * (2rh * dr/dt + r² * dh/dt)

Substituting the given values:

dV/dt = π * (2 * 1cm * 2cm * 0.2 cm/sec - 1cm² * 0.1 cm/sec)
       = π * (0.8 cm³/sec - 0.01 cm³/sec)
       = π * 0.79 cm³/sec

So, the rate of change of the volume of the cylinder is approximately 0.79π cm³/sec.

The radius of a right circular cylinder increases at the rate of 0.2 cm/sec and the height decreases at the rate of 0.1 cm/sec. The rate of change of the volume of the cylinder when the radius is 1cm and the height is 2cm is

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