Explanation:
The tube consists of a cylinder with a smaller cylinder removed from its center. We can find the volume of the tube by subtracting the volume of the smaller cylinder from the volume of the larger cylinder.
The volume of the larger cylinder is given by the formula:
V1 = πr^2h
where r is the radius and h is the height (or length) of the cylinder. Substituting the given values, we get:
V1 = π(3 cm)^2(20 cm) ≈ 565.49 cm^3
The volume of the smaller cylinder is also given by the formula:
V2 = πr^2h
where r is the radius (which is 1 cm in this case, since the diameter of the smaller cylinder is 2 cm less than the diameter of the larger cylinder) and h is the height (or length) of the cylinder (which is the same as the height of the larger cylinder). Substituting the given values, we get:
V2 = π(1 cm)^2(20 cm) ≈ 62.83 cm^3
Therefore, the volume of the tube is:
V = V1 - V2 ≈ 502.7 cm^3 (rounded to the nearest tenth)
Therefore, the volume of the tube is approximately 502.7 cubic centimeters.