Explanation Given: Let B be the solid whose base is a unit circle x 2 + y 2 = 1 and whose vertical cross section perpendicular to x -axis are equilateral triangles. Calculation: At any point x , the side of the equilateral cross section that lies in the unit circle base of the solid extends from the top half of the unit circle (with y = 1 − x 2 ) to the bottom half (with y = − 1 − x 2 ). Therefore, the length of the side (let us consider, s) of the equilateral triangle is; ⇒ s = ( 1 − x 2 ) − ( − 1 − x 2 ) = 2 1 − x 2 So, the area of equilateral triangle is given by; ⇒ A ( x ) = 3 4 ( s 2 ) = [ 3 4 ( 2 1 − x 2 ) 2 ] ∴ A ( x ) = 3 ( 1 − x 2

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.2, Problem 8E

To determine

Find the volume $V$ of solid $B$ whose base is a unit circle $x^{2} + y^{2} = 1$ and show that vertical cross section has area $A (x) = \sqrt{3} (1 - x^{2})$ .

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Chapter 6.2, Problem 7E

Chapter 6.2, Problem 9E

Chapter 6 Solutions

CALCULUS (CLOTH)

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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Prob. 39CRE Ch. 6 - Prob. 40CRE Ch. 6 - Prob. 41CRE Ch. 6 - Prob. 42CRE Ch. 6 - Prob. 43CRE Ch. 6 - Prob. 44CRE Ch. 6 - Prob. 45CRE Ch. 6 - Prob. 46CRE Ch. 6 - Prob. 47CRE Ch. 6 - Prob. 48CRE Ch. 6 - Prob. 49CRE Ch. 6 - Prob. 50CRE Ch. 6 - Prob. 51CRE Ch. 6 - Prob. 52CRE Ch. 6 - Prob. 53CRE Ch. 6 - Prob. 54CRE

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Find the volume V of solid B whose base is a unit circle x 2 + y 2 = 1 and show that vertical cross section has area A ( x ) = 3 ( 1 − x 2 ) .

Solution Summary: The author calculates the volume V of solid B, whose base is a unit circle x 2 + y 2 = 1 and its vertical cross section has area A (x) = 3

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Find the volume $V$ of solid $B$ whose base is a unit circle $x^{2} + y^{2} = 1$ and show that vertical cross section has area $A (x) = \sqrt{3} (1 - x^{2})$ .

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Chapter 6 Solutions

Find the volume V of solid B whose base is a unit circle x 2 + y 2 = 1 and show that vertical cross section has area A ( x ) = 3 ( 1 − x 2 ) .

Solution Summary: The author calculates the volume V of solid B, whose base is a unit circle x 2 + y 2 = 1 and its vertical cross section has area A (x) = 3

Videos

Find the volume V of solid B whose base is a unit circle x2+y2=1 and show that vertical cross section has area A(x)=3(1−x2).

Want to see the full answer?

Chapter 6 Solutions

Find the volume $V$ of solid $B$ whose base is a unit circle $x^{2} + y^{2} = 1$ and show that vertical cross section has area $A (x) = \sqrt{3} (1 - x^{2})$ .