Use the image below to answer the following questions.
(Desmos Calculator: Ctrl + select to open in a new tab)
(7th Grade Math Formula Chart: Ctrl + select to open in a new tab)
How to Determine the Surface Area of a Cylinder (Ctrl + link to open in a new tab)
(4 points)
Remember to use 3.14 for π
. Round to the nearest hundredths place (2 digits after the decimal).
Determine the area of the circular base of the cylinder.
square inches
Determine the width of the lateral face of the cylinder.
inches
Determine the area of the lateral face of the cylinder.
square inches
What is the total surface area of the cylinder?
square inches
radius is 7in and height is 14in
Area of the circular base of the cylinder:
Radius = 7 inches
Area = π(radius)^2 = 3.14 x 7^2 = 3.14 x 49 = 153.86 square inches
Width of the lateral face of the cylinder:
Perimeter of the base = 2π(r) = 2 x 3.14 x 7 = 43.96 inches
Area of the lateral face of the cylinder:
Width (perimeter) x Height = 43.96 x 14 = 615.44 square inches
Total surface area of the cylinder:
Area of the circular base + Area of the lateral face
= 153.86 + 615.44
= 769.30 square inches
is this answer rounded to the nearest hundredths place?
Apologies for the oversight. Let's round the answers to the nearest hundredths place.
Area of the circular base of the cylinder:
153.86 square inches
Width of the lateral face of the cylinder:
43.96 inches
Area of the lateral face of the cylinder:
615.44 square inches
Total surface area of the cylinder:
769.30 square inches
Therefore, all answers above are rounded to the nearest hundredths place.
is this only one of the circular bases?
I apologize for the confusion in my previous responses. The area of the circular base of the cylinder is actually represented twice in the total surface area calculation since a cylinder has two circular bases.
So, the corrected calculations are as follows:
Area of the circular base of the cylinder:
Radius = 7 inches
Area = π(radius)^2 = 3.14 x 7^2 = 3.14 x 49 = 153.86 square inches
Width of the lateral face of the cylinder:
Perimeter of the base = 2π(r) = 2 x 3.14 x 7 = 43.96 inches
Area of the lateral face of the cylinder:
Width (perimeter) x Height = 43.96 x 14 = 615.44 square inches
Total surface area of the cylinder:
Area of two circular bases + Area of the lateral face
= 2 x 153.86 + 615.44
= 307.72 + 615.44
= 923.16 square inches
Therefore, after considering both circular bases, the total surface area of the cylinder is 923.16 square inches rounded to the nearest hundredths place.