10. In cubic meters, how much greater is the volume of a cylinder with height 19 m and a radius 16 m than the volume of a square prism with height 19 m and base 16 m on a side?
Vc = pi*r^2 * h = 3.14*(16)^2 * 19 =
15,273m^3 = volume of cylinder.
Vp = Ab^2*h = (16)^2 * 19 = 4864m^3 =
volume of prism.
Vc - Vp = 15,273 - 4864 = 10,409m^3.
To determine the volume difference between a cylinder and a square prism with the given measurements, we need to calculate the volume of each shape separately and then find the difference.
The volume V of a cylinder is given by the formula: V = π * r^2 * h, where r is the radius of the cylinder's base and h is the height.
Step 1: Calculate the volume of the cylinder.
Given:
radius (r) = 16 m
height (h) = 19 m
Using the formula for the volume of a cylinder:
V_cylinder = π * 16^2 * 19
V_cylinder ≈ 15158.159 m^3 (rounding to the nearest cubic meter)
Next, we'll calculate the volume of the square prism.
The volume V of a rectangular prism is given by the formula: V = l * w * h, where l is the length, w is the width, and h is the height.
Step 2: Calculate the volume of the square prism.
Given:
base (side length) = 16 m
height (h) = 19 m
Using the formula for the volume of a rectangular prism:
V_prism = 16 * 16 * 19
V_prism = 4864 m^3
Finally, we can find the volume difference by subtracting the volume of the square prism from the volume of the cylinder.
Step 3: Find the volume difference.
Volume difference = V_cylinder - V_prism
Volume difference ≈ 15158.159 - 4864
Volume difference ≈ 10394.159 m^3
Therefore, the volume of the cylinder is approximately 10394.159 cubic meters greater than the volume of the square prism.