Question: A cone with height is inscribed in a larger cone with height H so that its vertex is at the center of the base of

A cone with height is inscribed in a larger cone with height H so that its vertex is at the center of the base of the larger cone. Show that the inner cone has maximum volume when h = 1/3H.

Step by Step Solution

★★★★★

3.23 Rating (181 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Vr 0 h h H By similar triangles 1 The volume of the inner cone is Hr V rh so well so... 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

Document Format (1 attachment)

M-C-D (444).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

The magnetic field B at the center of a circular coil of wire carrying a current l (as in Fig, 20-9) is Where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet...

A Texas cockroach first rides at the center of a circular disk that rotates freely like merry-go-round without external torques. The cockroach walk out the edge of the disk, at radius R. Figure gives...

A charged particle is held at the center of a spherical shell. Figure gives the magnitude E of the electric field versus radial distance r. The scale of the vertical axis is set by Es = 10.0 x 107...

Points: 0 of 1 Save A right circular cone is inscribed inside a larger right circular cone with a volume of 200 cm. The axes of the cones coincide, and the vertex of the inner cone tou the center of...

$$explain clearly... 2.4 Tangent Lines and Implicit Differentiation 1. At what point on the curve y = sinh r does the tangent line have a slope of 1? 2. Find the point(s) on the graph y = a where the...

Homework: 4 . 5 HW - Optimization Question Completed: 1 0 of 1 2 My score: 9 . 5 / 1 2 pts ( 7 9 . 1 7 % ) Problems A right circular cone is inscribed inside a larger right circular cone with a...

Project: Cone App Page 1 of 5 Deliverables Your project files should be submitted to Web-CAT by the due date and time specified. You may submit your files to the skeleton code assignment until the...

Files to submit to Web-CAT (both files must be submitted together): Cone.java ConeApp.java, Specifications Overview: You will write a program this week that is composed of two classes: (1) one named...

Can someone help me with that, and please if you don't know please just skip it leave it to someone who may know, because it's my fourth time to post, and they give me wrong answer, they just copy...

can some one do the ConeListApp.java please. Deliverables Your project files should be submitted to Web-CAT by the due date and time specified. You may submit your files to the skeleton code...

Compute a 98% confidence interval for the proportion of defective items in a process when it is found that a sample of size 100 yields 8 defectives.

What is the unit circle definition of sin ?

1. Salmon and tuna are substitutes in perfectly com- petitive markets that are experiencing long-run equilibrium. A. Suppose that an unforeseen change in the weather patterns of the Pacific Ocean...

On a hot summer day the temperature is 35C, barometric pressure is 103 kPa, and the relative humidity is 90%. An air conditioner draws in outside air, cools it to 20C, and delivers it at a rate of...

A firm has invested $14,000 in machinery with a 7- year useful life. The machinery will have no salvage value , as the cost to remove it will equal its scrap value. The uniform annual benefits from...

A small-business corporation is considering whether to replace some equipment in the plant. An analysis indicates there are five alternatives in addition to the do-nothing option, Alt. A. The...

A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval47

Model X100 sells for $120 per unit whereas Model X200 offers advanced features and sells for S500 per unit. Management expects to sell 50,000 units of Model X100 and 5,000 units of Model X200 next...

In a market without environmental regulations, will the supply curve for a firm account for private costs, external costs, both, or neither? Explain.

The radius of a right circular cone is increasing at a rate of 1.8 in/s while its height is decreasing at a rate of 2.5 in/s. At what rate is the volume of the cone changing when the radius is 120...

The length , width w, and height h of a box change with time. At a certain instant the dimensions are = 1 m and w = h = 2 m, and and w are increasing at a rate of 2 m/s while h is decreasing at a...

The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasing as the resistor heats up. Use Ohms Law, V = IR, to find how the...

Operating cash flow. Find the operating cash flow for the year for Harper Brothers, Inc it it had ales revenue of $303,700,000, cont of goods sold of $133,500,000 sales and administrative costs of...

Renkas Corp., a lamp manufacturer, provided the following information for the year ended December 31,2018 : (Click the icon to view account balances.) (Click the icon to view other information.)...

Assume that the duration of human pregnancies can be described by a Normal model with mean 265 days and standard deviation 13 days. a) What percentage of pregnancies should last between 271 and 284...