Justine needs to buy a cylinder, and she has three choices as shown. Cylinder A has a radius of 15 inches and a height of 22 inches. Cylinder B has a radius of 14 inches and a height of 23 inches. Cylinder C has a diameter of 24 inches and a height of 21 inches. Which cylinder has the greatest surface area, which would justify Justine buying it? Use 3.14 for pi
First, we need to calculate the surface area of each cylinder:
Cylinder A:
Surface area = 2πrh + 2πr^2
Surface area = 2(3.14)(15)(22) + 2(3.14)(15)^2
Surface area = 2(3.14)(330) + 2(3.14)(225)
Surface area = 2070.6 + 1413.0
Surface area = 3483.6 square inches
Cylinder B:
Surface area = 2πrh + 2πr^2
Surface area = 2(3.14)(14)(23) + 2(3.14)(14)^2
Surface area = 2(3.14)(322) + 2(3.14)(196)
Surface area = 2024.8 + 615.44
Surface area = 2640.24 square inches
Cylinder C:
First, we need to calculate the radius of Cylinder C:
Radius = diameter/2
Radius = 24/2
Radius = 12 inches
Surface area = 2πrh + 2πr^2
Surface area = 2(3.14)(12)(21) + 2(3.14)(12)^2
Surface area = 2(3.14)(252) + 2(3.14)(144)
Surface area = 1587.84 + 903.36
Surface area = 2491.2 square inches
Therefore, Cylinder A has the greatest surface area with 3483.6 square inches. Justine should buy Cylinder A if she wants to maximize the surface area.