Imagine slicing through a sphere with a plane (sheet of paper) The smaller piece produced is called a spherical cap Its volume is V h 2 (3r h) 3, where r is the radius of the sphere and h is the thickness of the cap a Find dr dh for a sphere with a volume of 5 3 b Evaluate this derivative when r 2 and h 1

Question: Imagine slicing through a sphere with a plane (sheet of paper). The smaller piece produced is called a spherical cap. Its volume is V =

Imagine slicing through a sphere with a plane (sheet of paper). The smaller piece produced is called a spherical cap. Its volume is V = πh²(3r - h)/3, where r is the radius of the sphere and h is the thickness of the cap.

a. Find dr/dh for a sphere with a volume of 5π/3.

b. Evaluate this derivative when r = 2 and h = 1.

Step by Step Solution

★★★★★

3.36 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

So so r 1 2rh ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus Early Transcendentals Questions!

The Excel worksheet form that appears below is to be used to recreate an example earlier in the chapter. Download the workbook containing this form from Connect. On the website you will also receive...

A single slice through a sphere of radius r produces a cap of the sphere. If the thickness of the cap is h, then its volume is V = 1/3 h 2 (3r - h). Graph the volume as a function of h for a sphere...

(a) Show that the volume of a segment of height h of a sphere of radius r is V = 1/3 Ïh2 (3r - h) h

The volume of a sphere is given by where V is the volume and r is the radius. If a certain sphere has a radius given as 0.005250 m, find its volume, specifying it with the correct number of digits....

nh'(3r h) Imagine slicing through a sphere with a plane (sheet of paper). The smaller piece produced is called a spherical cap. Its volume is V = 3 , where r is the radius of the sphere and h is the...

The experimental result differs from the assumption. The result shows that the ring oscillator frequencies can be grouped into two groups, where the first group is the high frequency group for the...

Please Follow the Instructions Subject English 103 Com/Critical Thinking 1. Analyze: In at least words , post a response to the assigned reading by analyzing the text (this is a close reading to find...

A glass sphere has radius R = 5.0cm and index of refraction 1.6. A paperweight is constructed by slicing through the sphere along a plane that is 2.0cm from the center of the sphere, leaving height h...

a glass sphere has radius R = 6 . 1 cm and index of refraction 1 . 7 . A paperweight is constructed by slicing through the sphere along a plance that is 2 . 0 cm from the center of the sphere, leaving

Question 4 of 10 - /1 ' View Policies Current Attempt in Progress A glass sphere has radius R = 5.9 cm and index of refraction 1.8. A paperweight is constructed by slicing through the sphere along a...

Imagine moving the hollow sphere of radius $R$ of Checkpoint $24.3 a$ sideways so that the charged object is no longer at the center of the sphere (but still within it). (a) How does the number...

Blast furnaces extract pure iron from the iron(III) oxide in iron ore in a two step sequence. In the first step, carbon and oxygen react to form carbon monoxide: 2C (s) + O 2 (g) 2CO (g) In the...

Incomplete linkage is A . Complete linkage is B . Choose the correct option for A and B. (A) A - common, B - rare (B) A - rare, B - common (C) A - impracticle, B - practicle (D) A - practicle, B -...

Which of the followitg thow how plying cash is leate oflice space for one year aftects the compungh financial etimemerti" \ table [ [ Payn e stmat,Incoue Statiment,Statement of Canh Blaw ] , [ ,...

20. Yield curve slope risk and duration risk can, for the most part, be managed independently because the correlation of changes in the level of rates and yield curve slope is very low.

Calculate the iterated integral. ye*- dx dy C2

Calculate the iterated integral. *7/2 1? sin' d dt *3

Calculate the iterated integral. C xy/r? + y dy dx

New Project Analysis The president of the company you work for has asked you to evaluate the proposed acquisition of a new chromatograph for the firms R&D department The equipment's basic price is...

2009 2010 Sales ($ millions) 1000 1112 Cost of Goods Sold ($ millions) 500 556 Other Expenses ($ millions) 100 111 Depreciation ($ millions) 100 100 Interest Expense ($ millions) 50 55 Total Current...

It appears that the per capita income elasticity of demand for natural gas is less than 1.0. a} If this is true, what term would we use to characterize the demand for natural gas? 1)) Using a 0.05...