A cone-shaped kitchen funnel has a diameter of 6 inches and a height of 7 inches. About how many times would you need to fill the funnel to fill a cylindrical can that has a radius of 4 inches and a height of 13 inches?
A. 3
B. 4
C. 9
D. 10
I don't really understand this question.
Can someone help?
Your funnel has a volume of
(1/3)π r^2 h = (1/3)π(3^2)(7) = .... cubic inches
one cylinder = π r^2 h = π(4^2)(13) = .....
How many times more is your second answer than the first?
It’s 10
idk the answer what is it?
Sure, I can help you understand and solve this problem step by step.
To begin, let's find the volume of the cone-shaped funnel. The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V represents the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base of the cone, and h is the height of the cone.
In this case, the diameter of the cone-shaped funnel is given as 6 inches, so the radius (r) is half of the diameter, which is 6/2 = 3 inches. The height of the cone is given as 7 inches.
Plugging these values into the volume formula, we get:
V_cone = (1/3) * π * (3 inches)^2 * 7 inches
V_cone = (1/3) * π * 9 square inches * 7 inches
V_cone = (1/3) * π * 63 cubic inches
V_cone ≈ 66.28 cubic inches (rounded to two decimal places)
Next, let's find the volume of the cylindrical can. The formula for the volume of a cylinder is V = π * r^2 * h, where V represents the volume, π is the mathematical constant approximately equal to 3.14159, r is the radius of the base of the cylinder, and h is the height of the cylinder.
In this case, the radius of the cylindrical can is given as 4 inches, and the height is given as 13 inches.
Plugging these values into the volume formula, we get:
V_cylinder = π * (4 inches)^2 * 13 inches
V_cylinder = π * 16 square inches * 13 inches
V_cylinder = π * 208 cubic inches
V_cylinder ≈ 653.34 cubic inches (rounded to two decimal places)
Now, to find out how many times we need to fill the cylindrical can with the funnel, we need to divide the volume of the cylindrical can by the volume of the funnel.
Number of fills ≈ V_cylinder / V_cone
Number of fills ≈ 653.34 cubic inches / 66.28 cubic inches
Number of fills ≈ 9.85 (rounded to two decimal places)
Therefore, the answer is approximately 9, so the correct option is C.