Math Question 2?

Question

The volume of a cylinder is given by V=Pi symbol^2h where r is the radius of the cylinder and h is the height of the cylinder. assume the volume of the can is 121 cubic cm.

write h as a function of r. Keep Pi in the functions equation.

what is the measurement of the height if the radius of the cylinder is 3 cm? Round to nearest hundredth's place

Answer 1

V = pi(r^2)h
h = V/[pi(r^2)]
V = 121cm^3
h = 121/[pi(r^2)]

r=3cm
h = 121/(9pi)
= 4.279cm (approx)
= 4.28cm (to the nearest hundredth)

Answer 2

Instead of putting cm^3 or cubic units, I'll leave just the numbers.
pir^2h=121
and instead of pi, I'll write x to make it easier for me.
xr^2h=121

Okay, let's see what we know.
When know that r can't be 0 or below 0, so r can be 1 or above.

Logically what happens is that as r increases, h decreases. The problem is how fast is it going down.
Let's find a few points on a graph of the x-axis as r and the y-axis as h.

This time I'll use 3.14 for pi
3.14(1^2)h=121
h~38.5
(1,38.5)
3.14(2^2)h=121
h~9.6
(2,9.6)
Okay, you can go on, but I'll tell you that this is exponentially going down.
Well, first find how h is compared to r
h=121/pir^2
f(r)=121/pir^2
f(r)=h
I'll say that f(r)=121/pi*r^-2
That is the function.

Answer 3

V = pi * r^2 * h Get h by itself on one side by dividing both sides of the equation by pi*r^2

V/pi*r^2 = h

h = 121/(3.14*3^2)
h = 121/28.26
h = 4.28 cm

Answer 4

V=Pi*h*r^2
h=V/(Pi*r^2)= 121/(Pi*3*3)= 4.2795