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    6. What is the volume of a regular square pyramid which has a total area of 360 if the square base is 10 on a side.

    9. How long is the edge of a cube whose total area is numerically equal to it's volume?

    15. A cube has a cylinder inscribed inside of it. That cylinder has a sphere inscribed inside of it. What is the ratio of the volume of the sphere to the volume of the cube?

    16.An equilateral triangle and a regular hexagon have equal perimeters. What is the ratio of the area of the triangle to the area of the hexagon?

    20. 240 spheres, each of radius 2, are placed in a box in 5 layers. There are 6 rows with 8 spheres in each row at each layer. The outside spheres are each tangent to the box and the spheres are tangent to those spheres next to them. Find the volume of the Box which is between the spheres.

    24. A cylinder is 10 inches high and has a total area of 150pie. What is it's volume?

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    6. What is the volume of a regular square pyramid which has a total area of 360 if the square base is 10 on a side.

    The Volume of a Pyramid = 1/3 × [Base Area] × Height
    The Surface Area of a Pyramid = 1/2 × Perimeter × [Side Length] + [Base Area]
    Here you're given Total area = 360 and base side = 10. We can get the side length first:

    360 = 0.5*4*10*sidelength + 100
    260 = 20*side length
    side length = 13

    Hence height =
    Thus volume of pyramid = 1/3*100*12= 400

    http://www.mathsisfun.com/geometry/pyramids.html

    9. How long is the edge of a cube whose total area is numberically equal to it's volume?

    Volume of cube = a3
    area of cube = 6a2
    We have a3 = 6a2
    Thus a = 6

    15. A cube has a cylinder inscribed inside of it. That cylinder has a sphere inscribed inside of it. What is the ratio of the volume of the sphere to the volume of the cube?

    The diameter of the sphere is equal to the length of the cube's edge.
    Volume of cube = a3
    Volume of sphere = 4/3*pi*(a/2)^3
    Thus = 0.52

    16. An equilateral triangle and a regular hexagon have equal perimeters. What is the ratio of the area of the triangle to the area of the hexagon?

    Let a and b be the sides of triangle and hexagon, respectively.
    Perimeter of triangle = 3a
    Perimeter of hexagon = 6b
    Thus 3a = 6b or a = 2b.
    Area of triangle =
    Area of hexagon =
    Thus:

    http://mathworld.wolfram.com/EquilateralTriangle.html

    http://en.wikipedia.org/wiki/Hexagon

    20. 240 spheres, each of radius 2, are placed in a box in 5 layers. There are 6 rows with 8 spheres in each row at each layer. The outside spheres are each tangent to the box and the spheres are tangent to those spheres next to them. Find the volume of the Box which is between the spheres.

    Diameter of sphere = 4
    Sides of the box:
    Length = 8*4 =32
    Width = 6*4 = 24
    Height = 5*4 = 20
    Thus volume = 32*24*20 = 15,360

    24. A cylinder is 10 inches high and has a total area of 150pie. What is its volume?
    Volume of cylinder = pi*r2*h
    Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h
    We're given h = 10
    150pi = 2pi*r2 + 2pi*r*h
    150 = 2r2 + 2rh
    75 = r2 + 10r
    Solving this quadratic equation gives r =5
    Thus volume = pi*25*10 = 250pi

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com September 26, 2022, 8:45 am ad1c9bdddf>
    https://brainmass.com/math/triangles/what-is-the-volume-of-a-regular-square-pyramid-which-has-a-t-118647

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