Maths question on a cylinder with a cone on top. What is question 3C asking and what’s the working?

As a design engineer, you are tasked with designing a liquid container comprising a cylinder with a cone at the top and the bottom is flat. The cylinder has a height of ℎ and radius of 𝑟, as illustrated in Figure Q3. The height and bottom radius of the cone are both 𝑟. Given the total volume, 𝑉, your objective is to design the container that minimises material usage. The width of the container walls is assumed to be negligible.

Hint: how do you calculate the surface area (A1) and volume (V1) of a cone? Please do some research and get the formulas.

3C. (8 marks)

What is the radius that minimises the surface area given a certain volume

As a design engineer, you are tasked with designing a liquid container comprising a cylinder with a cone at the top and the bottom is flat. The cylinder has a height of ℎ and radius of 𝑟, as illustrated in Figure Q3. The height and bottom radius of the cone are both 𝑟. Given the total volume, 𝑉, your objective is to design the container that minimises material usage. The width of the container walls is assumed to be negligible.

Hint: how do you calculate the surface area (A1) and volume (V1) of a cone? Please do some research and get the formulas.

3C. (8 marks)

What is the radius that minimises the surface area given a certain volume

Original post by H Forster

Maths question on a cylinder with a cone on top. What is question 3C asking and what’s the working?

As a design engineer, you are tasked with designing a liquid container comprising a cylinder with a cone at the top and the bottom is flat. The cylinder has a height of ℎ and radius of 𝑟, as illustrated in Figure Q3. The height and bottom radius of the cone are both 𝑟. Given the total volume, 𝑉, your objective is to design the container that minimises material usage. The width of the container walls is assumed to be negligible.

Hint: how do you calculate the surface area (A1) and volume (V1) of a cone? Please do some research and get the formulas.

3C. (8 marks)

What is the radius that minimises the surface area given a certain volume

As a design engineer, you are tasked with designing a liquid container comprising a cylinder with a cone at the top and the bottom is flat. The cylinder has a height of ℎ and radius of 𝑟, as illustrated in Figure Q3. The height and bottom radius of the cone are both 𝑟. Given the total volume, 𝑉, your objective is to design the container that minimises material usage. The width of the container walls is assumed to be negligible.

Hint: how do you calculate the surface area (A1) and volume (V1) of a cone? Please do some research and get the formulas.

3C. (8 marks)

What is the radius that minimises the surface area given a certain volume

What's your level of knowledge? As the question suggests, you'll need to know the formulae for volume and surface area of a cone; the final part is then a minimisation problem where one variable is a function of another one - what area of maths does this suggest to you?

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