Explanation:
volume of any type of pyramid :
1/3 × base area × height
FYI (not needed to solve the problem) :
base area is a pentagon.
the area of a pentagon is
1/2 × p × a
p is the perimeter (5 × side length) of the pentagon.
a is the apothem (the direct - right-angled- distance from the center of the pentagon to the center of a side).
volume of any type of regular prism :
base area × height
since the sides of the pentagon are the same, also their base areas are the same.
the height is the same.
so, when we compare both formulas, we see that the only difference is the factor 1/3.
the volume of the pyramid is 1/3 the volume of the prism.
therefore,
volume prism = volume pyramid × 3 = 435.7 × 3 =
= 1,307.1 cm³