calculus

The base of a solid is a circle of
radius = 4
Find the exact volume of this solid if the cross sections perpendicular to a given axis are equilateral right triangles.

The equation of the circle is:
x^2 + y^2 = 16

I have the area of the triangle (1/2bh) to be equal to 2sqrt(12)

(1/2 * 4 * sqrt12)

there are triangles that have vertical bases. They run parallel to the y-axis. The triangles are inside of the circle

Any help would be greatly appreciated! Thanks!


The volume of a cone is
V =(1/3)*(base area)*(height)

In your equilateral case,
height = sqrt3 * r.
Therefore
V = sqrt3*pi*r^3

  1. 👍 0
  2. 👎 0
  3. 👁 200
asked by mark
  1. 323

    1. 👍 0
    2. 👎 0
    posted by k

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc

    The base of a solid is a circle of radius a, and its vertical cross sections are equilateral triangles. The volume of the solid is 10 cubic meters. Find the radius of the circle.

    asked by Erica on February 10, 2011
  2. calculus

    1. A solid is constructed so that it has a circular base of radius r centimeters and every plane section perpendicular to a certain diameter of the base is a square, with a side of the square being a chord of the circle. a. Find

    asked by Yuri on March 25, 2012
  3. calculus

    The base of a solid is a circle of radius = 4 Find the exact volume of this solid if the cross sections perpendicular to a given axis are equilateral right triangles. I have the area of the triangle (1/2bh) to be equal to

    asked by mark on April 22, 2007
  4. Math

    The points (4, –5) and (– 4, 1) are endpoints of a diameter of a circle. (a) Find the center of the circle. (b) Find the length of the radius of the circle. (Note that this is a distance.) Give the exact answer. Show work. (c)

    asked by Kate on June 24, 2009
  5. calculus

    volume of solid whose base is a circle with radius a, and cross sections of the solid cut perpendicular to the x-axis are squares

    asked by judy on April 17, 2011
  6. geometry

    if home plate is 60.5 feet from the pitcher's mound, find the distance from the pitcher's mound of a major league baseball field to the center of a circumscribed circle that touches home plate, 1st base and second base. Find the

    asked by susan on October 16, 2011
  7. geometry

    I asked my teacher for a hint and he said that the pitcher's mound is not the radius. Am I supposed to assume that a side of a baseball diamond is 90? But that information wasn't given..... Still confused. If home plate is 60.5

    asked by susan on October 18, 2011
  8. maths

    Im confused can any1 help me on this question ?? or try and put me on the right track? (a) A circle has radius 2cm (in that circle there is an triangle AOB) and the chord AB has length 3cm. AO is 2cm and BO is 2cm. O is the centre

    asked by hi on September 25, 2007
  9. Calculus (cross section)

    A solid has a base bounded by x^2_y^2=36. Find the volume of the solid if every plane section perpendicular to the diameter is an isosceles triangle whose base is on the circle and whose height is 4 units

    asked by Trinh on November 30, 2014
  10. Geomatric series

    A fractal is created: A circle is drawn with radius 8 cm. Another circle is drawn with half the radius of the previous circle. The new circle is tangent to the previous circle. Suppose this pattern continues through five steps.

    asked by HanuMath25/11 on November 25, 2012

More Similar Questions