the volume of a right-circular cylinder is V = πr²h, however, this cylinder on 6) is not a right-circular cylinder, meaning, the its altitude is not going straight up making a right-angle with the ground, is all slanted.
now, let's recall Cavalieri's Principle,
solids with the same altitude and cross-sectional areas at each height have the same volume.
so, though this cylinder is slanted, its cross-sectional areas are the same as a right-circular cylinder and thus its volume is also V = πr²h, so yes, is correct.
7)
the area of a parallelogram is A = bh.
so the volume of this solid will simply be the area of the upfront parallelogram times the depth or length of 5x.
[tex]\bf (4x)(x+2)(5x)\implies (20x^2)(x+2)\implies 20x^3+40x^2[/tex]
