9514 1404 393
Answer:
583.4 cm³
Explanation:
We have the base dimensions, so enough information to find its area:
A = s²
A = (10 cm)² = 100 cm²
__
The height of the triangle is found by solving triangle AMV for the distance MV. That is found from the trig relation ...
Tan = Opposite/Adjacent
tan(68°) = MV/AM
The length of AM is half the diagonal of the square base, so is (10√2)/2 = 5√2. The length of MV is ...
MV = AM·tan(68°) = 5√2·tan(68°) ≈ 17.50
So, the volume of the pyramid is ...
V = (1/3)Bh
V = (1/3)(100 cm²)(17.50 cm) ≈ 583.4 cm³ . . . . volume of the pyramid