Question

Calling upon for Math help:

A cone has volume 36 pi.

a. If the cones radius is 1, what is its height?

b. If the cones radius is 2, what is its height?

c. If the cones radius is 6, what is its height?

Answer 1

Let me just google the formula for the volume of a cone

Answer 2

Okay!

Answer 3

\[V_{c} = \pi r \frac{ h }{ 3 }\]

Answer 4

It says the volume is 36 pi, which means we can say this:

\[36 \pi = \pi(1)\frac{ h }{ 3 }\]

Answer 5

For part a

Answer 6

Since pi is on both sides, we can divide the entire equation by pi, turning it into

\[36 = \frac{ h }{3 }\]

Answer 7

1 times h/3 = h/3, so I just simplified it there as well

Answer 8

Makes sense so far?

Answer 9

Yeah

Answer 10

Do you know what you'd do next?

Answer 11

Uhm, I am not sure.

Answer 12

In Algebra we want to isolate the variable, so we play with the numbers. However, in order to keep the equation true, whatever we do to one side, we do to the other. So what would get us h alone? Multiplying by 3

Since 3/3 = 1, and 1 times h is just h...

\[3(36) = \frac{ h }{ 3 } \times 3 \rightarrow 3(36) = h \times 1 \rightarrow 3(36) = h\]

Answer 13

Whatever 3 times 36 is, is the height

Answer 14

108?

Answer 15

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Shadow
It says the volume is 36 pi, which means we can say this:

\[36 \pi = \pi(1)\frac{ h }{ 3 }\]
\(\color{#0cbb34}{\text{End of Quote}}\)

One part I skipped over is that in the formula, it's actually r^2, so

\[V_{cone} = \pi r^2 \frac{ h }{ 3 }\]

But 1^2 is just 1 so I think my brain just kinda ignored it, but you'll need to respect the exponent for the other parts.

Answer 16

3 30s is 90, and 3 x 6 = 18, so yes

Answer 17

Okay! Thanks.

Answer 18

Do you feel confident you can tackle the others?

Answer 19

Yes, I do!

Answer 20

Cool

Answer 21

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Shadow
\[V_{c} = \pi r \frac{ h }{ 3 }\]
\(\color{#0cbb34}{\text{End of Quote}}\)
@Shadow excuse me but Volume formula of cone is area of base time height divide 3 so area of base will be pi*r^2 bc. is circle

Answer 22

@Astrid1 what is your question ?

Answer 23

Nvm, Shadow helped me!

Answer 24

ok np

yw