Question

A cylinder has a volume of 321 cubic units. If a cone has the same height and radius as the cylinder, what is its volume in cubic units?
A.
107 cubic units
B.
214 cubic units
C.
642 cubic units
D.
963 cubic units

Answer 1

u dont have to help if u dont want

Answer 2

It's okay! I like geometry (well until I get tired and then I don't wanna do complicated math LOL)

Do you need to use \(\pi\) here or 3.14?

Answer 3

no

Answer 4

❓

Answer 5

idk
nvm 3.14

Answer 6

Recap from last question - cylindrical volume \[V_{cylinder}=(3.14)r^2h\]

Answer 7

ye sry

Answer 8

np, take your time 😊
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Okay, so first we need to establish the dimensions. We are told that the cone "has the same height and radius as the cylinder" but we don't know the height OR radius of the cylinder. This makes things a little more complicated, but at least we have the cylinder's volume, \(321\text{ u}^3\).
Gathering all our data together, we have:\[\therefore V_{cylinder}=321\text{ u}^3=3.14r^2h\]and the values for \(r\) and \(h\) are the same in the cone volume formula,\[V_{cone}=\frac{1}{3}(3.14)r^2h\]

all good so far?

Answer 9

yes

Answer 10

okay, so we can see that there are some interesting similarities between these two equations:\[321\text{ u}^3=\color{royalblue}{3.14r^2h}\]and...\[V_{cone}=\frac{1}{3}\left(\color{royalblue}{3.14r^2h}\right)\]So that means we can do a substitution replacement, by putting 321 cube units instead of that whole mess. Then we would get:\[\therefore V_{cone}=\frac{1}{3}(321)=321\div3=107\]
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So your cone's volume is... 107 cube units, or \(107\text{ u}^3\)

Answer 11

so a

Answer 12

thanks kitt

Answer 13

np! 🎊