Question

The volume of a frustum of a cone is given by the formula \(V = \frac{1}{3}\pi z(x^2 + y^2 + xy)\, where \(x\) is the radius of the smaller circle, \(y\) is the radius of the larger circle, and \(z\) is the height of the frustum (see figure). Find the rate of change of the volume of this frustum when \(x = 2\) in, \(y = 4\) in, \(z = 2\) in, and each of these dimensions is changing at the rate of 0.5 in/min.

          The volume of a frustum of a cone is given by the formula
\(V = \frac{1}{3}\pi z(x^2 + y^2 + xy)\,
where \(x\) is the radius of the smaller circle, \(y\) is the radius of the larger circle, and \(z\) is the height of
the frustum (see figure). Find the rate of change of the volume of this frustum when \(x = 2\) in,
\(y = 4\) in, \(z = 2\) in, and each of these dimensions is changing at the rate of 0.5 in/min.

The volume of a frustum of a cone is given by the formula
V = (1)/(3)π z(x^2 + y^2 + xy)
where x is the radius of the smaller circle, y is the radius of the larger circle, and z is the height of
the frustum (see figure). Find the rate of change of the volume of this frustum when x = 2 in,
y = 4 in, z = 2 in, and each of these dimensions is changing at the rate of 0.5 in/min.

Added by Michael S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Pritesh Ranjan

Step 1

Given that y = 4 in and z = 2 in, we can substitute these values into the formula to find the volume of the frustum. V = (1/3)πh(y^2 + yz + z^2) V = (1/3)πh(4^2 + 4*2 + 2^2) V = (1/3)πh(16 + 8 + 4) V = (1/3)πh(28) V = (28/3)πh Show more…

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The volume of a frustum of a cone is given by the formula: V = (1/3)Ï€h(y^2 + yz + z^2) where y is the radius of the smaller circle, z is the radius of the larger circle, and h is the height of the frustum (see figure). Find the rate of change of the volume of this frustum when y = 4 in, z = 2 in, and each of these dimensions is changing at the rate of 0.5 in/min.