Question

Please please help me out

Answer 1

Answer:

The slant height of the pyramid is 3√2 ft, or to the nearest tenth ft,

4.2 ft

Step-by-step explanation:

The equation for the volume of a pyramid of base area B and height h is

V = (1/3)·B·h.  Here, V = 432 ft³, B = (12 ft)² and h (height of the pyramid) is unknown.  First we find the height of this pyramid, and then the slant height.

V = 432 ft³ = (144 ft²)·h, so h = (432 ft³) / (144 ft²) = 3 ft.

Now to find the slant height of this pyramid:  That height is the length of the hypotenuse of a right triangle whose base length is half of 12 ft, that is, the base length is 6 ft, and the height is 3 ft (as found above).

Then hyp² = (3 ft)(6 ft) = 18 ft², and the hyp (which is also the desired slant height) is hyp = √18, or √9√2, or 3√2 ft.

The slant height of the pyramid is 3√2 ft, or to the nearest tenth ft,

4.2 ft