To determine the diameter of a cylinder when you know its volume and height, you can use the formula for the volume of a cylinder:
Volume (V) = π × r² × h
Where:
- V = Volume of the cylinder (in cubic units)
- r = Radius of the cylinder (in units)
- h = Height of the cylinder (in units)
- π = Pi, approximately 3.14
In this case, you are given:
- V = 175 cubic units
- h = 7 units
Substituting the known values into the volume formula, we get:
175 = π × r² × 7
Now, to isolate r², we first divide both sides by 7:
r² = 175 / (π × 7)
Calculating the right side:
r² = 175 / (3.14 × 7)
r² = 175 / 21.98 ≈ 7.96
Next, we take the square root of both sides to find the radius:
r ≈ √7.96 ≈ 2.82 units
Finally, since diameter (d) is twice the radius:
d = 2 × r
d ≈ 2 × 2.82 ≈ 5.64 units
Thus, the diameter of the cylinder is approximately 5.64 units.