If the surface area of a cylinder is equal to the value of the volume of the cylinder. Find the value of x. X is the height which is unknown. The radius is 6ft
S=V
pi*r^2 + pi*r^2 + 2Pi*r*h=4/3 PI r^3
2r^2+2rh = 4/3 r^3
h= (4/3 r^2-2r)/2h check that. r=6, find h.
surface area = 2 circles + 1 rectangle
= 2π(36) + 2π(6)x
= 72π + 12πx
volume = π(36)x
36πx = 12πx + 72π
24x = 72
x = 3 <--- the height
To solve this problem, we need to set up the equation for the surface area and volume of a cylinder.
The formula for the surface area of a cylinder is:
SA = 2πrh + 2πr²
The formula for the volume of a cylinder is:
V = πr²h
Given that the surface area is equal to the volume, we can set up the equation:
2πrh + 2πr² = πr²h
Now let's substitute the given values into the equation:
2π(6)h + 2π(6)² = π(6)²h
12πh + 72π = 36πh
Rearranging the equation:
12πh - 36πh = -72π
-24πh = -72π
Dividing both sides of the equation by -24π:
h = 3
Therefore, the value of x (the height) is 3.
To solve this problem, we need to use the formulas for the surface area and volume of a cylinder.
The formula for the surface area (A) of a cylinder is given by:
A = 2πr² + 2πrh
Where:
r is the radius of the cylinder
h is the height of the cylinder
The formula for the volume (V) of a cylinder is given by:
V = πr²h
In this case, we are given that the surface area of the cylinder is equal to the volume of the cylinder. So we can set up the equation:
2πr² + 2πrh = πr²h
Substituting the given radius of 6ft into the equation, we have:
2π(6)² + 2π(6)x = π(6)²x
Simplifying the equation:
72π + 12πx = 36πx
Now, we can solve for x:
72π = 24πx
Dividing both sides of the equation by 24π:
72/24 = x
3 = x
Therefore, the height (x) of the cylinder is 3ft.