The height of a cylinder is three times the diameter of the base. The surface area of the cylinder is 126 t ft?. What is the radius of the base?
(1 point)
• 3ft
0 6ft
O9ft
• 18 ft.
To find the radius of the base, we first need to find the height of the cylinder.
Let the diameter of the base be D.
The height of the cylinder is given as three times the diameter, so height = 3D.
The surface area of a cylinder is given by the formula:
Surface Area = 2 * π * r * (r + h)
where r is the radius and h is the height.
Given that the surface area is 126π ft², we can substitute in the values and get:
126π = 2 * π * r * (r + 3D)
126 = 2 * r * (r + 3D)
126 = 2 * r * (r + 3D)
63 = r * (r + 3D)
Now, we need to find the relation between the radius r and the diameter D. Since r = D/2, we can substitute this in:
63 = (D/2) * (D/2 + 3)
Multiplying out:
63 = (D^2/4) + (3D/2)
252 = D^2 + 6D
D^2 + 6D - 252 = 0
We have a quadratic equation. By solving this equation, we get:
D = 12 or D = -18
Since the diameter cannot be negative, we discard the negative solution. Therefore, D = 12 ft.
Now to find the radius, we use r = D/2 = 12/2 = 6 ft.
Therefore, the radius of the base is 6 ft.