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14. (-/5 Points) DETAILS MY NOTES The volume $V$ of an ice cream cone is given by $V = \frac{2}{3}\pi R^3 + \frac{1}{3}\pi R^2h$ where $R$ is the common radius of the spherical cap and the cone, and $h$ is the height of the cone. The volume of the ice cream cone is increasing at the rate of 14 units$^3$/sec and its radius is increasing at the rate of $\frac{1}{10}$ units/sec when the radius $R$ and height $h$ are $(R, h) = (\frac{3}{2}, \frac{8}{2})$. At what rate is the height $h$ of the cone changing when $(R, h) = (\frac{3}{2}, \frac{8}{2})$? units/sec

          14. (-/5 Points) DETAILS MY NOTES
The volume $V$ of an ice cream cone is given by
$V = \frac{2}{3}\pi R^3 + \frac{1}{3}\pi R^2h$
where $R$ is the common radius of the spherical cap and the cone, and $h$ is the height of the cone.
The volume of the ice cream cone is increasing at the rate of 14 units$^3$/sec and its radius is increasing at the rate of $\frac{1}{10}$ units/sec when the radius $R$ and height $h$ are $(R, h) = (\frac{3}{2}, \frac{8}{2})$. At what rate is the height $h$ of the cone changing when $(R, h) = (\frac{3}{2}, \frac{8}{2})$?
units/sec

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14. (-/5 Points) DETAILS MY NOTES
The volume V of an ice cream cone is given by
V = (2)/(3)π R^3 + (1)/(3)π R^2h
where R is the common radius of the spherical cap and the cone, and h is the height of the cone.
The volume of the ice cream cone is increasing at the rate of 14 units^3/sec and its radius is increasing at the rate of (1)/(10) units/sec when the radius R and height h are (R, h) = ((3)/(2), (8)/(2)). At what rate is the height h of the cone changing when (R, h) = ((3)/(2), (8)/(2))?
units/sec

Added by Steven L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/06/2023

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Step 1: We are given that the volume V of the ice cream cone is given by the equation V = (1/3)πR^2h, where R is the common radius of the spherical cap and the cone, and h is the height of the cone. Show more…

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14. [-/5 Points] DETAILS The volume V of an ice cream cone is given by V= where R is the common radius of the spherical cap and the cone, and h is the height of the cone. The volume of the ice cream cone is increasing at the rate of 14 units^3/sec and its radius is increasing at the rate of 1/10 units/sec when the radius R and height h are (R, h) = (²-², 8) At what rate is the height of the cone changing when (R, h) = (²-², 8) units/sec? MY NOTES: - The text is missing the equation for the volume of the ice cream cone. - The word "heighth" should be "height". - The word "increan" should be "increasing". - The word "radus" should be "radius". - The word "rat" should be "rate". - The word "theradius" should be "the radius". - The word "Randheighthare" should be "R and height are". - The word "ingwhenRb" is unclear and should be corrected. - The word "s/sec" should be "units/sec".

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