4 Water drips into a conical container, which is orientated point downwards, at a rate of 100 mm³.s-1. The dimensions of the cone are such that the depth of water, h, is always equal to the radius, r, of the top surface of the water. ←→>>> h Show that the volume of the water is given by: V= V = 13h³ b) Find an expression for the rate of change of the depth of water with respect to time in terms of h. C) Find the rate at which the depth of water is increasing when the depth is 5 millimetres, giving the answer in mm.s¹ and to 3 significant figures.
4 Water drips into a conical container, which is orientated point downwards, at a rate of 100 mm³.s-1. The dimensions of the cone are such that the depth of water, h, is always equal to the radius, r, of the top surface of the water. ←→>>> h Show that the volume of the water is given by: V= V = 13h³ b) Find an expression for the rate of change of the depth of water with respect to time in terms of h. C) Find the rate at which the depth of water is increasing when the depth is 5 millimetres, giving the answer in mm.s¹ and to 3 significant figures.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Water drips into a conical container, which is orientated point downwards, at a rate
of 100 mm³.s-¹.
The dimensions of the cone are such that the depth of water, h, is always equal to
the radius, r, of the top surface of the water.
←1->>>
h
a)
Show that the volume of the water is given by:
V=
=h²³
b)
Find an expression for the rate of change of the depth of water with respect to
time in terms of h.
Find the rate at which the depth of water is increasing when the depth is 5
millimetres, giving the answer in mm.s¹ and to 3 significant figures.
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