Question

There is 1000cm^3 of aluminum available to cast a trophy that will be in the shape of a right square pyramid. Is the enough aluminum for a trophy that had a base edge of 10 cm and a slant height of 13 cm?

Answer 1

yes

Explanation:

The volume of the pyramid is given by ...

V = (1/3)Bh

where B is the base area, (10 cm)^2 = 100 cm^2, and h is the height.

We want to find the maximum height the pyramid may have, so ...

1000 ≥ (1/3)(100)h

30 ≥ h . . . . . . . . . divide by the coefficient of h

If the slant height of the pyramid is 13 cm, the height measured perpendicular to the base is less than that, so is less than 13 cm. We have enough aluminum to cast a trophy 30 cm high, so more than enough to cast the desired trophy.

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Comment on height

The slant height is the hypotenuse of a right triangle with leg lengths 5 and 12. The height of the desired trophy is 12 cm, but you don't need to know that to answer the question. You only need to know that 30 > 13 > desired height.