Math

posted by .

A monument consists of two cubical blocks of granite, the smaller resting on the larger. The total height of the monument is 5 feet, and the area of the exposed surface is 61 square feet. Find the dimensions of the blocks.

Help please>.< Thank you in advance!

  • Math -

    length of side of the larger --- x
    length of side of the smaller -- y

    x+y = 5

    So what do we see?
    We see 4 side faces of the larger = 4x^2
    we see 4 side faces of the smaller = 4y^2
    If we look straight down, we see a small face on top of the large face exposing the edge of the large face not covered by the smaller cube.
    But isn't that just equal to the surface area of the large top?

    so 5x^2 + 4y^2 = 61
    from x+y=5 ---> y = 5-x
    5x^2 + 4(25-10x+x^2) = 61
    5x^2 + 100 - 40x + 4x^2 = 61
    9x^2 -40x + 39=0
    (x-3)(9x-13) = 0
    x = 3 or x = 13/9

    the blocks could be 3ft for the larger, and 2 ft on each side for the smaller
    or
    the larger be have a side of 32/9 and the smaller 13/9 ft

  • Math -

    can you provide a check for the answers?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra

    A surveyor is standing 115 feet from the base of the Washington Monument. The sureyor measures the angle of elevation to the top of the monument as 78.3. How tall is the Washington Monument?
  2. Math

    Jack is standing next to a monument in the city square. His shadow is 18 feet long. The shadow of the monument is 150 feet long. If Jack is 6 feet tall, how tall is the monument
  3. math

    the dimensions of a rectangular prism are height 7 feet, width 4 feet and length 3 feet find the surface area part 2: dimensions of the cylinder are height 7 feet and radius 3.5 feet solve with a decimal then round to the nearest half …
  4. math

    The Washington Monument is the tallest structure in Washington D.C. At the same time the monument casts a shadow that is about 500 feet long, a 40 foot flagpole nearby casts a shadow that is about 36 feet long. Make a sketch. Find …
  5. geometry

    Marc is visiting washington dc he wants to know the height of the washington monument the length of the monument shadow is 111 feet long at the same time that marcs shadow is 1 foot long Marc is 5 feet tall using this data find the …
  6. early trig

    A monument stands on level ground. The angle of elevation of the top of the monument, taken at a point 425 feet from the foot of the monument, is 32ยบ. Find the height of the monument to the nearest foot.
  7. Math

    Mr. Hemley stands next to the Illinois Centennial Monument at Logan Square in Chicago and casts a shadow that is 18 feet long. The shadow of the monument is 204 feet long. If Mr.Hemley is 6 feet tall, how tall is the monument?
  8. PHYSICS

    explorers in the jungle find an ancient monument in the shape of a large isosceles triangle. the monument is made from tens of thousands of small stone blocks of density 3 800 kg/m^3. the monument is 15.7 m high and 64.8 m wide as …
  9. math

    The Washington monument is 555 feet high. If you are standing one quarter of a mile, or 1320 feet, from the base of the monument and looking at the top, find the angle of elevation to the nearest degree.
  10. Math

    A monument has a base and a statue. The base is a rectangular prism that measures 4 feet by 6 feet by 2 feet. The statue is a cube with edges that are 2 feet long. What is the volume of the monument?

More Similar Questions