A conical scoop is used to remove coffee from the can an place it into a coffee maker. the scoop has a 1 inch diameter and a 2 inch height. if one level scoop is used to make each cup of coffee, how many cups of coffee can be made from a full 2-pound can of coffee? the can's dimensions are; diameter-6in height-6.25 in
would you divide the volumes?
To determine the number of cups of coffee that can be made from a full 2-pound can of coffee, we need to compare the volumes of the scoop and the can.
First, let's calculate the volume of the conical scoop. The formula to find the volume of a cone is given by:
Volume = (1/3) * π * r^2 * h
where r is the radius of the base (half the diameter) and h is the height.
Given that the diameter of the scoop is 1 inch, the radius (r) of the scoop is 1/2 inch. And the height (h) of the scoop is 2 inches.
Plugging these values into the formula, we get:
Volume of the scoop = (1/3) * π * (1/2)^2 * 2
= (1/3) * π * (1/4) * 2
= (1/6) * π
Now let's calculate the volume of the can. The formula to find the volume of a cylinder is given by:
Volume = π * r^2 * h
where r is the radius of the base and h is the height.
Given that the diameter of the can is 6 inches, the radius (r) of the can is 6/2 = 3 inches. And the height (h) of the can is 6.25 inches.
Plugging these values into the formula, we get:
Volume of the can = π * 3^2 * 6.25
= π * 9 * 6.25
= 56.25 * π
Now, to find the number of cups of coffee that can be made, we divide the volume of the can by the volume of the scoop:
Number of cups of coffee = (Volume of the can) / (Volume of the scoop)
= (56.25 * π) / (1/6 * π)
= 56.25 * 6
= 337.5
Therefore, you can make approximately 337.5 cups of coffee from a full 2-pound can of coffee using one level scoop per cup. Since you can't make a fraction of a cup, you would round down the answer, in this case, to 337 cups.
yes. Think of the units:
in^3/can / in^3/cup = cup/can
volume of can: pi*3^2*6.25 = 450pi/8
volume of scoop: 1/3 pi * (1/2)^2 * 2 = pi/6
450pi/8 / pi/6 = 1350/4 = 337.5