BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is dr…

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Question

Chapter 5.2, Problem 79E

To determine

To solve the formula for the volume of a sphere, for r .

Expert Solution

Answer to Problem 79E

The formula solved for r=3V4π3 .

Explanation of Solution

Given information:

The given statement is:

“You have filled two round balloons with water. One balloon contains twice as much water as the other balloon.”

Solve the formula for the volume of sphere V=43πr3 , for r .

Formula used:

The formula used is:

V=43πr3

Calculation :

The solution can be obtained by:

V=43πr3r3=3V4πr=3V4π3

Hence, the formula solved for r=3V4π3 .

To determine

To substitute the formula for r into the formula of surface area of the sphere.

Expert Solution

Answer to Problem 79E

The expression after substitution is S=4π(3V4π3)2 .

Explanation of Solution

Given information:

The given statement is:

“You have filled two round balloons with water. One balloon contains twice as much water as the other balloon.”

Surface area of the sphere S=4πr2 . Simplify to show that S=(4π)1/3(3V)2/3

Formula used:

The formula used is:

S=4πr2

Calculation :

The formula for surface area after substitution is S=4π(3V4π3)2

The solution can be obtained by:

S=4π(3V4π3)2S=4π(3V)2/3(4π)2/3S=4π1−2/3(3V)2/3S=4π1/3(3V)2/3

Hence, the expression after substitution is S=4π(3V4π3)2 .

To determine

To compare the surface area of the two water balloons using the formula.

Expert Solution

Answer to Problem 79E

The surface area of the larger balloon is 22/3=1.59 times the surface of the smaller balloon.

Explanation of Solution

Given information:

The given statement is:

“You have filled two round balloons with water. One balloon contains twice as much water as the other balloon.”

Surface area of the sphere S=(4π)1/3(3V)2/3

Formula used:

The formula used is:

S=(4π)1/3(3V)2/3

Calculation :

The surface area of the larger balloon is 22/3=1.59 times the surface of the smaller balloon.

Chapter 5.2, Problem 78E

Chapter 5.2, Problem 80E

Chapter 5 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - 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The surface area and volume of cone, cylinder, prism and pyramid; Author: AtHome Tuition;https://www.youtube.com/watch?v=SlaQmaJCOt8;License: Standard YouTube License, CC-BY