Question

How do you do these problems? And is the first one done right?

Answer 1

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.

`\bf (4x)(x+2)(5x)\implies (20x^2)(x+2)\implies 20x^3+40x^2`