Find the volume of the cone if the heights of the solids are equal and the cross sectional areas at every level parallel to the respective bases are also equal. Round to the nearest hundredth.

If the heights are equal and the cross-sectional areas are equal, then the volumes are equal.

For the pyramid:

at h=0, A = 9ft * 8ft = 72 ft²

at h = 17ft/2, A = ½ * 9ft * ½ * 8ft = 18 ft²

at h = 17ft, A = 0.

Then A (h) = 72ft² * (17 - h) ²/289 = (72ft²/289) (289 - 34h + h²)

Then V = ∫[a, b] A (h) dh = ∫[0,17] (72ft²/289) (289 - 34h + h²) dh

V = (72ft²/289) (289h - 17h² + h³/3) |[0,17]

V = (72ft²/17²) (17³ - 17³ + 17³/3) = 72ft² * 17/3 = 408 ft³

(Or did you simply know that the volume of a rectangular pyramid is

V = basearea * height / 3