Question: A right circular cone is inscribed in a sphere, as shown. (a) The sphere has centre O and radius 12 cm. A is the

A right circular cone is inscribed in a sphere, as shown. (a)

A right circular cone is inscribed in a sphere, as shown. (a) The sphere has centre O and radius 12 cm. A is the vertex of the cone, B is a point on the base of the cone that touches the sphere and, C is the centre of the base of the cone. :0 Let |OC|=x. Find | BC|, the radius of the cone, in terms of x. (i) Show that the volume of the cone is equal to (12 + x)(12 x). (ii) (iii) Hence find the maximum volume of the cone, in terms of T.

Step by Step Solution

★★★★★

3.55 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Lets tackle this step by step i Find BC the radius of the cone in terms of x 1 Identify Triangle OBC ... 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 Mathematics Questions!

A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder.

A right circular cone is to be inscribed in another right circular cone of given volume, with the same axis and with the vertex of the inner cone touching the base of the outer cone. What must be the...

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...

You will be expected to put together a financial plan based on either a real small business, or a fictitious one (data may be supplied by instructor). While each plan is unique depending on the...

Please help I dont get it 3 4 6 Jake buys a bag of popcorn at a movie theater. He eats half of the popcorn during the 15 minutes of If 20 - x = 15, what is the value of 3x ? 8 previews. After eating...

270 Chapter 4 Applications of Derivatives c. What is the largest area the rectangle can have, and what are its dimensions? 12. Find the volume of the largest right circular cone that can be in- X...

Please answer all 24 of these practice geometry questions, thanks! 1. (198) Which of the following statements is false? A. A cone is a lot like a pyramid, except that it has a circular base. B. The...

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

1. The following equation represents the volume of a box created from a sheet of paper that is 8 in x 11 in after congruent squares are cut from each corner: V = (8 -2x) (11 -2x) (2) Given that 'x'...

Hello, I have having a difficult time answering number eight. And if you have the time could you perhaps check if my other work is correct? It'd be super useful, thanks for any help! 8/11/2020 Apex...

The 2-Mg bridge, with center of mass at point G, is lifted by two beams CD, located at each side of the bridge. If the 2-Mg counterweight E is attached to the beams as shown, determine the angle ?...

What are three main reasons it is better to design quality into a process than to find problems upon inspection?

Express the repeating decimal as the ratio of two integers. 1 . 5 1 7 8 9 Continuing = 1 . 5 1 7 8 9 7 8 9 7 8 9 . . .

Margaret and David Simmons are married and file a joint income tax return. They have two dependent children, Margo, 5 years old (Social Security number 316-31-4890), and Daniel, who was born during...

Brian Cleary and Rita Burke filed a suit against the major cigarette maker Philip Morris USA, Inc., seeking class-action status for a claim of deceptive advertising. Cleary and Burke claimed that...

Carlton Tennis Clubs adjusted trial balance at the end of its fiscal year follows. Required 1. Prepare T accounts and enter the balances for J. Kojas, Capital; J. Kojas, Withdrawals; Income Summary,...

Open Text Corporation's financial statements contain the following selected data (in U.S. $ millions): _______________________2015______________2014 Total...

Part 1. Meir, Benson, and Lau are partners and share income and loss in a 3:2:5 ratio. The partnerships capital balances are as follows: Meir, $ 168,000; Benson, $ 138,000; and Lau, $ 294,000. Benson...

Respond to this Greetings, Brazil and Switzerland present very different economic landscapes that influence how companies manage working capital and make financing decisions. Brazil, with its...

Solve the following problem with and without calculus. A good picture helps. a. A cube with side length r is inscribed in a sphere, which is inscribed in a right circular cone, which is inscribed in...

Three-dimensional sprites The glshapes.* files in the Pop Framework provide some standard 'glut' methods for drawing three-dimensional shapes. 'Glut' stands for 'OpenGL...

9. (1 point) A cup of coffee at 181 degrees is poured into Note: Express your answer as a positive speed. a mug and left in a room at 72 degrees. After 7 minutes, the 12. (1 point) A spherical...

Use python 3.6 please A right circular cone is a 3-dimensional shape that has 2 key dimensions: 1. The base radiusr 2. The height - h An illustration of a right circular cone with these dimensions...

Cones come in a few varieties, and we will consider the right circular cone. A cone with a circular base is a circular cone. A circular cone whose axis is perpendicular to the base is a right...

Exercise 4 The lateral surface area of a right-circular cone (a right cone with a base that is a circle) can be calculated by the function: f:h, r f(h, r); f(h, r) = ar 1p +h where h is the height of...