Using linearization to calculate the thickness of a layer of paint on a spherical ballCalculate the fraction of volume of a rectilinear grid cell within some radius of the originVolume of a sphere “corner”What is the volume of the sphere in hyperbolic space?How to write the volume element for a spherical shell?How to calculate the volume of intersection of sphere and cylinderVolume of part (not necessary the half) of spherical capcomputing volume of unit ball in n-dimensions using polar coordinatesWhat will the volume of the ball bearing be?Calculus related rates snowball radius problemWidth of layer formed from sphere $r = n$ fitted inside sphere $r = 4n$
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Using linearization to calculate the thickness of a layer of paint on a spherical ball
Calculate the fraction of volume of a rectilinear grid cell within some radius of the originVolume of a sphere “corner”What is the volume of the sphere in hyperbolic space?How to write the volume element for a spherical shell?How to calculate the volume of intersection of sphere and cylinderVolume of part (not necessary the half) of spherical capcomputing volume of unit ball in n-dimensions using polar coordinatesWhat will the volume of the ball bearing be?Calculus related rates snowball radius problemWidth of layer formed from sphere $r = n$ fitted inside sphere $r = 4n$
$begingroup$
The volume of a sphere with radius $r$ is given by the formula $V(r) = frac4 pi3 r^3$.
a) If $a$ is a given fixed value for $r$, write the formula for the linearization of the volume function $V(r)$ at $a$.
b) Use this linearization to calculate the thickness $Delta r$ (in $cm$) of a layer of paint on the surface of a spherical ball with radius $r=52cm$ if the total volume of paint used is $340cm^3$.
The first part is easy to calculate, but I don't know exactly how to get the second part?
derivatives volume linear-approximation
asked Dec 11 '15 at 15:41
Essi A.Essi A.
61
$endgroup$
bumped to the homepage by Community♦ yesterday
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
add a comment |
$begingroup$
The volume of a sphere with radius $r$ is given by the formula $V(r) = frac4 pi3 r^3$.
a) If $a$ is a given fixed value for $r$, write the formula for the linearization of the volume function $V(r)$ at $a$.
b) Use this linearization to calculate the thickness $Delta r$ (in $cm$) of a layer of paint on the surface of a spherical ball with radius $r=52cm$ if the total volume of paint used is $340cm^3$.
The first part is easy to calculate, but I don't know exactly how to get the second part?
derivatives volume linear-approximation
asked Dec 11 '15 at 15:41
Essi A.Essi A.
61
$endgroup$
bumped to the homepage by Community♦ yesterday
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
add a comment |
$begingroup$
The volume of a sphere with radius $r$ is given by the formula $V(r) = frac4 pi3 r^3$.
a) If $a$ is a given fixed value for $r$, write the formula for the linearization of the volume function $V(r)$ at $a$.
b) Use this linearization to calculate the thickness $Delta r$ (in $cm$) of a layer of paint on the surface of a spherical ball with radius $r=52cm$ if the total volume of paint used is $340cm^3$.
The first part is easy to calculate, but I don't know exactly how to get the second part?
derivatives volume linear-approximation
asked Dec 11 '15 at 15:41
Essi A.Essi A.
61
$endgroup$
The volume of a sphere with radius $r$ is given by the formula $V(r) = frac4 pi3 r^3$.
a) If $a$ is a given fixed value for $r$, write the formula for the linearization of the volume function $V(r)$ at $a$.
b) Use this linearization to calculate the thickness $Delta r$ (in $cm$) of a layer of paint on the surface of a spherical ball with radius $r=52cm$ if the total volume of paint used is $340cm^3$.
The first part is easy to calculate, but I don't know exactly how to get the second part?
derivatives volume linear-approximation
derivatives volume linear-approximation
asked Dec 11 '15 at 15:41
Essi A.Essi A.
61
asked Dec 11 '15 at 15:41
Essi A.Essi A.
61
asked Dec 11 '15 at 15:41
Essi A.Essi A.
61
asked Dec 11 '15 at 15:41
Essi A.Essi A.
61
asked Dec 11 '15 at 15:41
Essi A.Essi A.
61
61
bumped to the homepage by Community♦ yesterday
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
bumped to the homepage by Community♦ yesterday
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
The volume $Delta V$ of paint is approximatively given by
$$Delta V=V(a+Delta r)-V(a)doteq V'(a)>Delta r=4pi a^2>Delta r .tag1$$
In your problem the unknown is the thickness $Delta r$ of the paint layer. From $(1)$ we immediately get
$$Delta rdoteqDelta Vover 4pi>a^2 .$$
answered Dec 11 '15 at 21:21
Christian BlatterChristian Blatter
175k8115327
$endgroup$
$begingroup$
thanks a lot for the quick reply
$endgroup$
– Essi A.
Dec 12 '15 at 4:14
add a comment |
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1 Answer
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1 Answer
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$begingroup$
The volume $Delta V$ of paint is approximatively given by
$$Delta V=V(a+Delta r)-V(a)doteq V'(a)>Delta r=4pi a^2>Delta r .tag1$$
In your problem the unknown is the thickness $Delta r$ of the paint layer. From $(1)$ we immediately get
$$Delta rdoteqDelta Vover 4pi>a^2 .$$
answered Dec 11 '15 at 21:21
Christian BlatterChristian Blatter
175k8115327
$endgroup$
$begingroup$
thanks a lot for the quick reply
$endgroup$
– Essi A.
Dec 12 '15 at 4:14
add a comment |
$begingroup$
The volume $Delta V$ of paint is approximatively given by
$$Delta V=V(a+Delta r)-V(a)doteq V'(a)>Delta r=4pi a^2>Delta r .tag1$$
In your problem the unknown is the thickness $Delta r$ of the paint layer. From $(1)$ we immediately get
$$Delta rdoteqDelta Vover 4pi>a^2 .$$
answered Dec 11 '15 at 21:21
Christian BlatterChristian Blatter
175k8115327
$endgroup$
$begingroup$
thanks a lot for the quick reply
$endgroup$
– Essi A.
Dec 12 '15 at 4:14
add a comment |
$begingroup$
The volume $Delta V$ of paint is approximatively given by
$$Delta V=V(a+Delta r)-V(a)doteq V'(a)>Delta r=4pi a^2>Delta r .tag1$$
In your problem the unknown is the thickness $Delta r$ of the paint layer. From $(1)$ we immediately get
$$Delta rdoteqDelta Vover 4pi>a^2 .$$
answered Dec 11 '15 at 21:21
Christian BlatterChristian Blatter
175k8115327
$endgroup$
The volume $Delta V$ of paint is approximatively given by
$$Delta V=V(a+Delta r)-V(a)doteq V'(a)>Delta r=4pi a^2>Delta r .tag1$$
In your problem the unknown is the thickness $Delta r$ of the paint layer. From $(1)$ we immediately get
$$Delta rdoteqDelta Vover 4pi>a^2 .$$
answered Dec 11 '15 at 21:21
Christian BlatterChristian Blatter
175k8115327
answered Dec 11 '15 at 21:21
Christian BlatterChristian Blatter
175k8115327
answered Dec 11 '15 at 21:21
Christian BlatterChristian Blatter
175k8115327
answered Dec 11 '15 at 21:21
Christian BlatterChristian Blatter
175k8115327
175k8115327
$begingroup$
thanks a lot for the quick reply
$endgroup$
– Essi A.
Dec 12 '15 at 4:14
add a comment |
$begingroup$
thanks a lot for the quick reply
$endgroup$
– Essi A.
Dec 12 '15 at 4:14
$begingroup$
thanks a lot for the quick reply
$endgroup$
– Essi A.
Dec 12 '15 at 4:14
$begingroup$
thanks a lot for the quick reply
$endgroup$
– Essi A.
Dec 12 '15 at 4:14
add a comment |
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