Anonymous asked in Science & MathematicsMathematics · 1 month ago

Math help please?

I need help solving these math problems, please.

1) Two bookends are in the shape of a trapezoidal prism. Each's made of marble.

The dimensions of the prism are left side height 18.5 cm, length 20 cm, width 7.5 cm, and right side height 15 cm. The bottom half is shaped like a cube and the top half is a triangle that slants downward (left side height 18.5 cm, and the right side where it tapers off is height is cm)

a) What's the volume of marble in one book end?

b) An artist has a 0.25 cubic meters of marble. How many sets of bookcases can be made?

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2 Answers

  • TomV
    Lv 7
    1 month ago
    Favorite Answer

    a) The volume is equal to the area of the front/rear face multiplied by the thickness.

    A = (18.5 + 15)(20)/2 = 335 cm²

    V = At = 335*7.5 = 2512.5 cm³ in one bookend

    b) Assuming the dimensions of the 0.25 m² marble block are topologically compatible with the dimensions of the bookend such that there is minimum wastage:

    0.25 m³ = 0.25(100³) cm³

    n = 0.25(100³)/2512.5 = 99.5

    The artist can make 99 individual bookends or 99/2 = 49 complete sets of bookends

    The remaining scrap (marble pieces and sawdust) will be equivalent to the volume of 1.5 individual bookends.

  • 1 month ago

    bottom half is shaped like a cube ?? no, it is not even close. A cube has equal dimensions.

    but if you take the area of one side, the sum of the rectangle and triangle, and multiply by the depth, you will have the volume

    making some assumptions about right angles, see below.

    A = 20•15 + (1/2)(18.5–15)(20)

    A = 300 + (1/2)(3.5)(20)

    A = 300 + 35

    V = 7.5A = 7.5(335) = 2512.5 cm³

    b) An artist has a 0.25 cubic meters of marble. How many sets of bookcases can be made?

    2512.5 cm³ x (1 m/100 cm)³ = 2.51e-3 m³

    0.25 / 2.51e-3 m³ = 99.50249

    so he can make 99 pieces, or 49 pairs

    (if you rounded volume number to 2500 cm³ , you could get 50 as the answer)

    this is a very simplistic answer which doesn't take wastage into account, plus saw kerf. Real life, you could probably get 40.

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