You want to fill the cylinder shown below with water. All you have is a container shaped like a cone with a radius of 3 inches and a height of 7 inches; you can use this cone-shaped container to take water from a faucet and fill the cylinder. How many cones will it take to fill the cylinder? Explain your reasoning.

n = 9.14 ≈ 10 cones (if integer is required)

Step-by-step explanation:

Given:

- The dimensions of the cylinder "missing from this question" are:

Radius r_1 = 8 in, Height h_1 = 3 in

- The dimensions of faucet are:

Radius r_2 = 3 in, Height h_2 = 7 in

Find:

- How many cone shaped like containers are required to fill the cylinder.

Solution:

- We will denote the letter 'n' as the number of cone shaped containers.

- For n amount of cone shaped containers is to fill the container the volume of water of n container should equal the volume of water in cylinder. This can be expressed as follows:

n*V_cone = V_cylinder

- Where,

V_cone = (1 / 3) * pi * r^2 _2 * h_2

V_cylinder = pi*r^2_1*h_1

- Hence,

n = V_cylinder / V_cone

Plug in values:

n = (3*r^2_1 * h_1) / r^2_2 * h_2

n = (3 * 8^2 * 3) / (3^2 * 7)

n = 576 / 63 = 9.14 cones

Answer: n = 10 cones