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? Choose the closest answer rounded to the nearest tenth.
3
10
9
4
9
To find out how many times you would need to fill the funnel to fill the cylindrical can, you need to calculate the volume of each.
The volume of a cone is given by the formula:
V_cone = (1/3) * π * r^2 * h
where r is the radius and h is the height of the cone.
Given that the diameter of the kitchen funnel is 6 inches, the radius would be half of that, which is 3 inches. The height of the funnel is 7 inches. Plugging these values into the formula:
V_cone = (1/3) * π * 3^2 * 7
V_cone = (1/3) * π * 9 * 7
V_cone = (1/3) * π * 63
V_cone ≈ 66.3 in^3 (rounded to one decimal place)
The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
where r is the radius and h is the height of the cylinder.
Given that the radius of the cylindrical can is 4 inches and the height is 13 inches, plugging these values into the formula:
V_cylinder = π * 4^2 * 13
V_cylinder = π * 16 * 13
V_cylinder = π * 208
V_cylinder ≈ 652.3 in^3 (rounded to one decimal place)
To find out how many times you would need to fill the funnel to fill the cylindrical can, you can divide the volume of the cylinder by the volume of the cone:
Number of fills = V_cylinder / V_cone
Number of fills ≈ 652.3 / 66.3
Number of fills ≈ 9.8 (rounded to one decimal place)
Therefore, you would need to fill the funnel about 9 times to fill the cylindrical can. The closest answer rounded to the nearest tenth is 9.
To find out how many times you need to fill the funnel to fill the cylindrical can, we need to compare their volumes.
The volume of a cone is given by the formula:
V_cone = (1/3) * π * r^2 * h
where r is the radius of the base of the cone and h is the height of the cone.
And the volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
where r is the radius of the base of the cylinder and h is the height of the cylinder.
First, let's find the volume of the cone:
Given:
Diameter of the cone = 6 inches
Radius of the cone (r_cone) = 6 / 2 = 3 inches
Height of the cone (h_cone) = 7 inches
Using the formula of the cone's volume:
V_cone = (1/3) * π * r_cone^2 * h_cone
V_cone = (1/3) * π * 3^2 * 7
V_cone = (1/3) * π * 9 * 7
V_cone = (1/3) * π * 63
V_cone ≈ 66.2 cubic inches (rounded to the nearest tenth)
Next, let's find the volume of the cylinder:
Given:
Radius of the cylindrical can (r_cylinder) = 4 inches
Height of the cylindrical can (h_cylinder) = 13 inches
Using the formula of the cylinder's volume:
V_cylinder = π * r_cylinder^2 * h_cylinder
V_cylinder = π * 4^2 * 13
V_cylinder = π * 16 * 13
V_cylinder = π * 208
V_cylinder ≈ 652.2 cubic inches (rounded to the nearest tenth)
To determine how many times we need to fill the funnel to fill the cylindrical can, we divide the volume of the cylindrical can by the volume of the cone:
Number of times to fill the funnel = V_cylinder / V_cone
Number of times to fill the funnel ≈ 652.2 / 66.2
Number of times to fill the funnel ≈ 9.9
Rounded to the nearest tenth, the answer is approximately 10.
Therefore, the closest answer rounded to the nearest tenth is 10.