Tingles wants to sell potato chips in cylindrical containers. So the chips do not fall out the containers will have ends. To be environmentally conscious, the company president wants to make the container entirely out of cardboard. Furthermore, they will choose the cylinder that is made with the least amount of cardboard. Cylinder A has a diameter of 4 inches and a height of 2.5 inches. Cylinder B has a diameter of 2 inches and a height of 10 inches. Which containter will they choose?
Answer choices
1. Container B
2. Container A
well, the area of a cylinder is
a = π/2 d(d+2h)
you can forget the 2π, since that is a constant factor of both cylinders. So, plug your numbers into
d(d+2h)
and see which is greater.
To determine which container Tingles should choose, we need to calculate the surface area of each cylinder as this will give us an indication of the amount of cardboard required.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr^2 + 2πrh
where r is the radius and h is the height.
For Container A:
Radius (r) = diameter/2 = 4/2 = 2 inches
Height (h) = 2.5 inches
Surface Area (A) = 2π(2^2) + 2π(2)(2.5)
= 8π + 20π
= 28π square inches
For Container B:
Radius (r) = diameter/2 = 2/2 = 1 inch
Height (h) = 10 inches
Surface Area (B) = 2π(1^2) + 2π(1)(10)
= 2π + 20π
= 22π square inches
Comparing the surface areas, we can see that Container B (22π square inches) has a smaller surface area than Container A (28π square inches).
Therefore, Tingles should choose Container B as it requires the least amount of cardboard.