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17 March, 12:10

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then its volume is:

A) 36

B) 12sqrt3

C) 18sqrt3

D) 24sqrt3

E) 36sqrt3

The correct answer was E. Hoping someone could explain how that is.

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Answers (1)
  1. 17 March, 14:09
    0
    Letter E is correct.

    Area of equilateral trianlge = (1/2) tiime a^2 square root 3

    Equation for the base is = x^2+y^2 = 9

    at x,

    y = square root (9-x^2)

    Side of triangle a = 2y

    d times Volume = (1/2) a^2 square root 3 dx

    d times V = (square root 3) (9-x^2) dx

    V = square root 3 INT (9-x^2) dx

    -3V = 2square root INT (9-x^2) dx

    0

    V = 2 square root 3 (9x-x^3/3)

    V=2 square root 3 (27-9)

    V = 36 square root 3

    The answer is E.
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