a storage bin is shaped like a cylinder with a hemisphere shaped top. the cylinder is 45 inches tall. the volume of the bin is 4131 pi cubic inches. find the radius of the bin.
i think [4(pi)r(cubed)]/3=volume of hemisphere
and h (pi) r squared volume of the cylinder.
so
[4(pi) r (cubed)/3] + [45 (pi) r squared= volume of bin
so
[4 r (cubed)/3] + [45 (pi) r squared=volume
how do i solve for r?
sorry, i'm stuck
the volume of a sphere is 4/3 PI r^3, so a hemisphere would be half of that.
If you have an equation such as this,
a r^3 + b r^2 + c=0
it is a third degree equation. I think I would graph
f(r)= a r^3+b r^2+c and see where it crosses the axis, that is a solution.
There are ways to solve cubic equations, but for this, I would graph it.
thanks Mr. Pursley,
graphing it now.
To solve for the radius, we can rearrange the equation and solve for r.
The equation you have is:
(4πr^3)/3 + 45πr^2 = volume
Since the volume is given as 4131π cubic inches, we can substitute that into the equation:
(4πr^3)/3 + 45πr^2 = 4131π
Now, let's eliminate the common factor of π:
(4r^3)/3 + 45r^2 = 4131
To solve for r, we can rearrange the equation in a standard form:
4r^3 + 135r^2 - 4131 = 0
This is now a cubic equation. Unfortunately, there isn't a simple formula to solve such an equation. However, we can use numerical methods or approximations to find an estimate of r.
To solve for the radius (r) of the storage bin, we can start by simplifying the equation you set up:
[4r³/3] + [45πr²] = volume of the bin
First, let's substitute the given volume value into the equation:
[4r³/3] + [45πr²] = 4131π
Now, let's remove the π term by dividing both sides of the equation by π:
[4r³/3π] + [45r²] = 4131
Next, let's multiply both sides of the equation by 3 to eliminate the fraction:
4r³ + 135πr² = 3 * 4131
Combine the terms on the right side:
4r³ + 135πr² = 12393
Now, to solve for r, we can rearrange the equation:
4r³ + 135πr² - 12393 = 0
Unfortunately, this is a cubic equation, which can be a bit more challenging to solve compared to linear or quadratic equations. There are various methods to solve cubic equations, such as factoring, using the rational root theorem, or numerical methods like Newton's method.
In this case, it may be more convenient to use numerical methods or a graphing calculator to find an approximate solution for r.