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.

  1. 👍
  2. 👎
  3. 👁
  1. Since we cannot draw the figure here, you can draw the figure yourself.
    Note that a right pyramid is a pyramid with a square base and the apex (the tip of the pyramid) is aligned directly at the center of the base.
    Now, draw an line from the apex to the center of the base, which serves as the height of the pyramid. Then connect the center of the base to one of the midpoints of the side of the square. The slant height is from that midpoint to the apex.
    Note that you have formed a right triangle, where the height is unknown, and the hypotenuse (which is also the slant height) is 15 cm. You can solve for the base of the right triangle by getting the half of the side of the square, which is 6 cm.
    Solving for height, recall pythagorean theorem. For any right triangle,
    a^2 + b^2 = c^2
    where
    a = base of right triangle
    b = height of right triangle
    c = hypotenuse
    Substituting,
    6^2 + b^2 = 15^2
    36 + b^2 = 225
    b^2 = 189
    b = 3*sqrt(21) cm [height]

    Recall that the volume of ANY pyramid is just
    V = (Area of the base)*(height)/3
    *Area of the base = (length of side of square)^2
    V = (12^2)*[3*sqrt(21)]/3
    V = 144*sqrt(21) cm^3

    Recall that the SA of a SQUARE pyramid is just
    SA = 2bs + b^2
    where
    s = slant height
    b = length of side of square
    SA = 2*12*15 + 12^2
    SA = 504 cm^2

    Hope this helps~ :)

    1. 👍
    2. 👎
  2. Part(a)

    Base of square =12cm
    Slant height of pyramid =15cm

    [Applying the theorem]

    (Height)^2+6^2=15^2
    (Height)^2=225-36
    (Height)^2=189
    Height=189^2
    Height= (square root of189)
    = 13.74cm

    Part(b). :. volume of pyram
    =1/3×base area×h
    Volume of pyramid =1/3×12^2×13.74cm^3
    =659.52cm^3

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    the great pyramid of cheops is a square based pyramid with a height of 147 meters and a base length of 230 meters. find the angle to the nearest degree that one of the edges of the pyramid makes with the base

  2. Math

    The base of a pyramid-shaped tank is a square with sides of length 12 feet, and the vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at the rate of 2

  3. Math

    Ira built a model of the great pyramid in Egypt for a school project. The great pyramid had a square base with sides of length 756feet the height of the great pyramid is 481 feet Ira made his model pyramid using a scale of 1 inch

  4. Mathematics

    In the adjoining figure,the slant height and the total surface area of square based pyramid are 12cm and340sq.cm respectively.find the perimeter of the base and volume

  1. MATH! PLEASE REPLY ASAP!

    OPQRS is a regular square-pyramid whose base has sides of 7 cm. Given that the total surface area of the pyramid is 161 cm2, find its slant height.

  2. Maths

    A right pyramid on a base 4cm square has a slant edge of 6cm.calculate the volume of the pyramid

  3. Mathematics

    A pyramid with vertical height of 1ocm stands on a square base of sides 20cm . a. Calculate to 3 significant figure for its total surface area. b. If the pyramid is hollow what it's capacity in litres.

  4. geometry

    a pyramid has a square base that measures 3 feet on each side. the height of the pyramid is 19 inches. what is the volume?

  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? Will the

  2. math

    The base of a regular pyramid is a square whose sides have a length 8 cm. If a lateral edge of this pyramid has length 20 cm, what is the surface area of the pyramid?

  3. Geometry

    The base of a regular pyramid is a hexagon whose sides have length 5 ft. If a lateral edge of this pyramid has length 9 ft, what is the surface area of the pyramid?

  4. AP CALCULUS!! HELPPP URGENT

    related rates: the base of a pyramid-shaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the

You can view more similar questions or ask a new question.