Question

The height of a cylinder is 3 times larger than the radius. Find the volume of the cylinder as a function of the height. (V = πr^2h)

Answer 1

Same thing here...we have

\[\large V = \pi r^2 h\]

We know that the height is 3 times larger than the radius...so

\[\large h = 3r\]
This means that the radius is 3 times smaller than the height...so we have
\[\large r = \frac{h}{3}\]

Now we can replace 'r' in our first equation here...with the 'h/3'

\[\large V = \pi (\frac{h}{3})^2h\]

And simplify from there

Answer 2

would it be V=1/3 πr^2?

Answer 3

i mean to the third power

Answer 4

Not quite...it should be a function of 'height' right? so the only variable should be 'h' in there right?

Answer 5

lol yes sorry my mistake

Answer 6

We have

\[\large V = \pi(\frac{h}{3})^2h\]

Remember that
\[\large (\frac{h}{3})^2 = \frac{h^2}{3^2} = \frac{h^2}{9}\]

so we have
\[\large V = \pi \frac{h^2}{9}h \]
\[\large V = \pi \frac{h^3}{9}\]

Answer 7

V = 3πh^3
V = 9πh^3
V =1/9 πh^3
V =1/3πh^3

Answer 8

mmhmm same thing as

\[\large V = \frac{1}{9}\pi h^3\]:)

Answer 9

ohhhh okay lol thanks again ;*

Answer 10

Haha you're welcome again ;)