Erik states that the two cones below have the same volume because of Cavalieri’s principle. 2 cones are shown. The first cone has a radius of r, a slant length of c, and a height of b. The second cone has a radius of r, a height of a, and a slant length of b. Is Erik’s statement correct? Why or why not? Yes, the solids are both cones and appear to have the same volumes. Yes, the area of the bases and the heights of the cones are the same, so the volumes are equal. No, the heights of the cones are not the same, so Cavalieri’s principle does not apply.

D. No, the heights of the cones are not the same, so Cavalieri’s principle does not apply.

Step-by-step explanation:

Correct on Edge.

The person above me is correct but the option is C.

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}