math

posted by .

looking at a square pyramid, if the size of the base remains the same and the height of the pyramid varies what are the minimum surface area and minimum volume the pyramid can have? The base is showing 2 in and the line on the right side of the base which I believe is also still the bottom of the pyramid shows 2 in. the height indicator inside the pyramid has the right angle marking on it but there is no number listed for that height.

I am confused on how to do surface area and volume if V=1/3bh and we don't know the height? Same with trying to figure out the surface area?

  • math -

    I suspect you are missing something in the problem statement but

    the base seems to be square, 2 by 2 so the base area = 4

    then the volume v is 1/3 *the area of the base * the height
    v = (1/3)4 h

    I assume the surface area you mean is the area of the sides, not including the base.
    Look at one of the sloping sides. Its base is 2 but we need to find its altitude by using trig. It is the hypotenuse of a triangle whose base is 1 and height is h
    therefore the altitude is sqrt(1+h^2)
    therefore the area of one side is
    (1/2)(2)(sqrt(1+h^2))
    and the total area of all four sides is
    4 sqrt(1+h^2)

    so v = 4/3 h
    the minimum is of course when h = 0

    a = 4 (1+h^2)^.5
    da/dh = 4(.5)(1+h^2)^-.5 * 2h
    this is clearly zero when h = 0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    A pyramid has a square base with sides length of b. The height of the pyramid is h. If the pyramid is enlarged by doubling the height while leaving the base unchanged, what is the effect on the volume of the pyramid?
  2. Mathematics

    OPQRS is a right pyramid whose base is a square of sides 12cm each. Given that the slant height of the pyramid is 15cm. Find the height of the pyramid, the volume of the pyramid, and the total surface area of the pyramid by first drawing …
  3. geometry

    The base of a pyramid is a square. The perimeter of the base is 20ft, and the surface area of the pyramid is 65ft^2. Find the slant height of the pyramid.
  4. Maths

    Solve the equation:a right pyramid with vertical height stand on rectangular base widith that measures 20cm by 14cm the hieght of the pyramid is 10cm calculate to 3 significant figure the length of the slant height , the surface area …
  5. Maths

    OPQRS is a right pyramid whose base is a square of sides 12cm each. Given that the slant height of the pyramid is 15cm. Find the height of the pyramid. The volume of the pyramid and the total surface of the pyramid.
  6. Maths

    OPQRS is a right pyramid whose base is a square of sides 12cm each. Given that the slant height of the pyramid is 15cm. Find the height of the pyramid. The volume of the pyramid and the total surface of the pyramid.
  7. Math

    The entrance hall to the Louvre Museum in Paris is a glass and metal pyramid with a surface area of approximately 1980 square on each side . The base of the pyramid is a square that is 35.4 meters on each side. What is the slant height …
  8. math

    The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid …
  9. math

    The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid …
  10. Math

    The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid …

More Similar Questions