Answer:
Step-by-step explanation:
The radius of a cone is the radius of its circular base. You can find a radius through its volume and height. Multiply the volume by 3. For example, the volume is 20.
So triangle has 3 sides
represent them as x,y,z
so lets say x=shortest side
y=2nd side
z=longest side
x is 1/2 of the second side
x=1/2(y)
shortest side is 1/3 of the longset side
x=1/3(z)
how does the triangle compart the longest side (z)
x+y+z=perimiter
solve to subsitute and convert all values to z
x=1/2y
2x=y
2(1/3z)=y
2/3(z)=y
and x=1/3(z)
therefor, subsitute so that there are only z terms
1/3(z)+2/3(z)+z=perimiter
add like terms
3/3(z)+z=p
z+z=p
2z=p
the peimiter is 2 times of the longest side
The volume of the cylinder from the rectangle is the size of the cylinder
The rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
<h3>How to determine the rectangle</h3>
Let the dimension of the rectangle be x and y.
So, the perimeter (P) is:
The perimeter is given as 18.
So, we have:
Divide both sides by 2
Make y the subject
The volume of a cylinder is:
So, we have:
Expand
Differentiate
Set to 0
Divide both sides by
Divide both sides by 3x
Make x the subject
Recall that:
So, we have:
Hence, the rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
Read more about volumes at:
brainly.com/question/10171109