Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
2nd Edition
ISBN: 9780618912407
Author: MCDOUGAL LITTEL
Publisher: Mcdougal Littel
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Expert Solution & Answer
Chapter 2.8, Problem 44PS
Solution
To find: What is the maximum volume of the cylinder?
The volume of cylinder as a function of h would be V=π4(256h−h3) . The value of h would be approximately 9.24 . The maximum volume of the cylinder is about 1238 cubic units.
Given information:
A cylinder is inscribed in a sphere of radius 8.
Formula used:
Volume of cylinder is πr2h , here r represents radius and h represents height of the cylinder.
Calculation:
First of all, find the radius of cylinder using Pythagoras theorem. Draw a right triangle as shown below:
Here D is diameter of the cylinder. Using Pythagoras theorem, the set-up would be:
D2=(8+8)2−h2D2=162−h2D2=256−h2D=√256−h2
It is known that radius is half the diameter, so radius of the cylinder would be r=√256−h22 .
V=πr2h=π(√256−h22)2h=πh(256−h24)=π4(256h−h3)
Therefore, the volume of cylinder as a function of h would be V=π4(256h−h3) .
Upon graphing the volume function, the required graph would look like as shown below:
It is visible that the maximum volume is about 1238 cubic units and occurs when x≈9.238 , therefore, the value of h that maximizes the volume would be 9.24 units.
Chapter 2 Solutions
Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
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- A television show tests the abilities of alleged psychics by presenting contestants with a set of \[4\] cards placed upside down, \[1\] of which has a star printed on it. Each contestant attempts to identify which card has the star on it for a series of \[50\] trials. Assuming that the contestants are purely guessing, what are the mean and standard deviation of the number of trials where the contestant guesses correctly?You may round your answers to the nearest tenth.arrow_forwardA television show tests the abilities of alleged psychics by presenting contestants with a set of \[4\] cards placed upside down, \[1\] of which has a star printed on it. Each contestant attempts to identify which card has the star on it for a series of \[50\] trials. Assuming that the contestants are purely guessing, what are the mean and standard deviation of the number of trials where the contestant guesses correctly?You may round your answers to the nearest tenth.arrow_forwardA large fast-food chain runs a promotion where \[1\]-in-\[4\] boxes of french fries include a coupon for a free box of french fries. Suppose that some location sells \[100\] of these boxes of fries per day. Let \[X=\] the number of coupons won per day. Find the mean and standard deviation of \[X\].You may round your answers to the nearest tenth.arrow_forward
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- 22.) Mr. Vedrani has a pool with a deck built around it. The equation (2x+14)(2x+19) = 650 represents the relationship of the side lengths (in feet) of the entire pool area (in square feet). a.) If 350 represents the area of the pool and deck area, what do the expressions (2x+14) and (2x+19) each represent? b.) Using graphing technology, find x, the width of the deck around the pool. If necessary, round to the nearest tenth. x=arrow_forwardHow do I get common factors?arrow_forwardProblem #1 You apply to two different graduate programs at a specific university: one in geology and one in environmental sciences. Let P(G) = 0.8, where P(G) represents the probability that you get accepted into the geology program. Let P(E) = 0.72, where P(E) represents the probability that you get accepted into the environmental sciences program. Let P(GE) = 0.65. a). Create a Venn diagram that represents this information. b). First, calculate P(GUE). Then, using complete sentence, interpret what P(GUE) represents in the context of this problem.arrow_forward
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