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

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.

hkhkhkhkhkhkhk

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.