Final answer:
The function rule for the volume of a cylinder with a height 3 inches more than 4 times the radius is V = πr²(4r + 3). For a radius of 2 inches, the volume is 44π cubic inches or approximately 138.2304 cubic inches.
Step-by-step explanation:
The function rule for the volume of a cylinder where the height is 3 inches more than 4 times the radius can be written using the formula for the volume of a cylinder, V = πr²h. Here, if r represents the radius, then the height h will be h = 4r + 3. Substituting h into the volume formula, we get the function rule as V = πr²(4r + 3).
When the radius is 2 inches, using the function rule:
V = π(2 inches)² × (4(2 inches) + 3 inches)
V = π(4 in²) × (8 inches + 3 inches)
V = π × 4 in² × 11 inches= 44π in³
The volume when the radius is 2 inches is 44π cubic inches, which can be approximated using π = 3.1416 to 138.2304 cubic inches.