Final answer:
To find the diameter of a cylinder with a volume of 310.86yd³ and height of 11yd, solve for the radius using the formula V = πr²h and then double it. The diameter is approximately 9.998 yd.
Step-by-step explanation:
The question asks for the diameter of a cylinder with a known volume and height, using the formula for the volume of a cylinder V = πr²h. First, we need to solve for the radius (r) of the cylinder and then double it to get the diameter. Given that V is approximately 310.86 yd³ and h is 11 yd, using 3.14 for π, we rearrange the formula to solve for r:
V = πr²h
r² = V / (πh)
r² = 310.86 yd³ / (3.14 × 11 yd)
r = √(310.86 yd³ / (3.14 × 11 yd))
r ≈ 4.999 yd
Therefore, the diameter is:
Diameter = 2r ≈ 2 × 4.999 yd ≈ 9.998 yd
The diameter of the cylinder is approximately 9.998 yd.