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) The rate of change of the volume is determined using $\frac{\partial V}{\partial x} \Delta x + \frac{\partial V}{\partial y} \Delta y + \frac{\partial V}{\partial z} \Delta z$ (i) $\Delta V \approx$ $\frac{dV}{dt} \approx \frac{\partial V}{\partial x}\frac{dx}{dt} + \frac{\partial V}{\partial y}\frac{dy}{dt} + \frac{\partial V}{\partial z}\frac{dz}{dt}$ (ii) The rate of change of the volume of this frustum when x increases at a rate of a cm/s, y decreases at a rate of b cm/s and z remains constant is The rate of change of the volume of this frustum in terms of $\pi$, a and b when x = 2 cm, y = 2 cm and z = 3 cm is

          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)
The rate of change of the volume is determined using
$\frac{\partial V}{\partial x} \Delta x + \frac{\partial V}{\partial y} \Delta y + \frac{\partial V}{\partial z} \Delta z$
(i) $\Delta V \approx$
$\frac{dV}{dt} \approx \frac{\partial V}{\partial x}\frac{dx}{dt} + \frac{\partial V}{\partial y}\frac{dy}{dt} + \frac{\partial V}{\partial z}\frac{dz}{dt}$
(ii)
The rate of change of the volume of this frustum when x increases at a rate of
a cm/s, y decreases at a rate of b cm/s and z remains constant is
The rate of change of the volume of this frustum in terms of $\pi$, a and b when
x = 2 cm, y = 2 cm and z = 3 cm is

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)
The rate of change of the volume is determined using
(∂ V)/(∂ x)Δ x + (∂ V)/(∂ y)Δ y + (∂ V)/(∂ z)Δ z
(i) Δ V ≈
(dV)/(dt)≈(∂ V)/(∂ x)(dx)/(dt) + (∂ V)/(∂ y)(dy)/(dt) + (∂ V)/(∂ z)(dz)/(dt)
(ii)
The rate of change of the volume of this frustum when x increases at a rate of
a cm/s, y decreases at a rate of b cm/s and z remains constant is
The rate of change of the volume of this frustum in terms of π, a and b when
x = 2 cm, y = 2 cm and z = 3 cm is

Added by Inmaculada M.

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