If a cylindrical container has a volume of cubic feet, then its surface

area S in square feet (excluding the top and bottom) is given by S = s=(2π )/r where r is the radius of the cylinder.

(a) Calculate S when r =1/2 foot
(b) What happens to this surface area when r becomes large? Sketch this situation

My Eq for surface area(excluding top and bottom) does not agree with yours.

My Eq: S = 2pi*rh.
r = radius.
h = height.

Please check your Eq.

a. S = 2*3.14*0.5*h = 3.14h.

b. The surface ara increases with r.

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A cylinder has a surface area of 250cm2. The height is twice as big as the radius. What is the height of the cylinder?

To calculate the surface area (S) of a cylindrical container, we can use the formula S = (2π) * r, where r is the radius of the cylinder.

(a) Let's calculate S when r = 1/2 foot:
S = (2π) * (1/2) = π square feet
Therefore, when the radius is 1/2 foot, the surface area of the cylinder (excluding the top and bottom) will be π square feet.

(b) When the radius becomes large, the surface area increases significantly. This can be shown by sketching the situation. As the radius increases, the circumference of the cylinder also increases, resulting in a larger surface area.

Imagine a cylinder with a small radius, and another cylinder with a larger radius. The small cylinder would have a smaller surface area compared to the larger cylinder. As the radius continues to increase, the surface area of the cylinder will also increase.

In the sketch, draw two cylinders side by side, one with a small radius and the other with a large radius. Label the surface area on each cylinder and compare them. As the radius becomes larger, you will see that the surface area also increases.

It's important to note that the surface area of the cylinder can approach infinity as the radius continues to increase, meaning it becomes infinitely larger.