57 418
Assignments Done
Successfully Done
In February 2018
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Calculus Question for Anandi

Question #13357
find the volume of the largest circular cone that can fit in a sphere of radius 3 cm.
Expert's answer
The volume of a right circular cone is V = 1/3 π r2 h. To apply the calculus you know you need to express this volume as a function of one variable. The right triangle ABC give the information you need.

R = radius sphere
r = base radius cone
R + h = height cone
V = volume cone

V = (1/3)πr²(R + h)

By the Pythagorean Theorem:
r² = R² - h²

Plug into the formula for volume.
V = (1/3)π(R² - h²)(R + h) = (1/3)π(R³ + R²h - Rh² - h³)

Take the derivative and set equal to zero to find the critical points.

dV/dh = (1/3)π(R² - 2Rh - 3h²) = 0
R² - 2Rh - 3h² = 0
(R - 3h)(R + h) = 0
h = R/3, -R

But h must be positive so:
h = R/3

Calculate the second derivative to determine the nature of the critical points.

d²V/dh² = (π/3)(-2R - 6h) < 0
So this is a relative maximum which we wanted.

Solve for r².
r² = R² - h² = R² - (R/3)² = R²(1 - 1/9) = (8/9)R²

Calculate maximum volume.

V = (π/3)[(8/9)R²](R + R/3) = (8/27)πR³(4/3) = 32πR³/81

For R = 3 maximum volume is:

V = 32π(3³)/81 = 32π(27)/81 = 32π/3

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be first!

Leave a comment

Ask Your question