The silo below is half-a-sphere on top of a cylinder. The container (including the top) is will be filled up to 81% capacity. What will the filled volume be? (The figure is not drawn to scale.)
base = 26
height = 101
incorrect. go back to mathematics class.
who else shall answer?
the post just below this one is the same question, but with different numbers.
Follow its method, but check the math -- the bot is notoriously often incorrect.
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To determine the filled volume of the silo, we need to calculate the volume of the half-sphere on top of the cylinder and then find 81% of that volume.
Step 1: Calculate the volume of the cylinder
The volume of a cylinder is given by the formula V_cylinder = π * r^2 * h, where r is the radius of the base and h is the height of the cylinder.
Given that the radius is half the base, we can calculate the radius (r) as r = base / 2 = 26 / 2 = 13.
Now, substitute the values into the formula: V_cylinder = π * 13^2 * 101.
Step 2: Calculate the volume of the half-sphere
The volume of a half-sphere is given by the formula V_half-sphere = (2/3) * π * r^3, where r is the radius of the sphere.
The radius of the half-sphere is equal to the radius of the base of the cylinder, which is 13 in this case.
Now, substitute the radius into the formula: V_half-sphere = (2/3) * π * 13^3.
Step 3: Calculate the total filled volume
To find the total filled volume, we add the volume of the cylinder to the volume of the half-sphere.
Total volume = V_cylinder + V_half-sphere.
Finally, multiply the total volume by 81% to get the filled volume: filled volume = total volume * 0.81.
Now, you can substitute the values and perform the calculations to find the filled volume.
volume of cylinder = πr2h = π(13)2(101) = 34,937.7 cubic meters
volume of hemisphere = 2/3πr3 = 2/3π(13)3 = 11,854.2 cubic meters
total volume = 46,791.9 cubic meters
filled volume = 81% of 46,791.9 = 37,851.5 cubic meters