Answer:
25%
Step-by-step explanation:
To find what percent of the total surface area (excluding the base of the jar) is blue, we need to use the formula for the surface area of a cylinder, excluding one circular base.
The formula for this is:
[tex]\large\boxed{\textsf{SA of cylinder (excluding one base)} = \pi r^2 + 2\pi rh}[/tex]
where r is the radius of the circular base, and h is the height of the cylinder.
[tex]\dotfill[/tex]
Blue Surface Area
The radius and height of the blue part are:
Therefore, the surface area of the blue part is:
[tex]SA = \pi \cdot 2^2+2\pi \cdot 2 \cdot 1\\\\SA = 4\pi +4\pi \\\\SA=8\pi\; \sf in^2[/tex]
[tex]\dotfill[/tex]
Total Surface Area
The radius and height of the entire jar and lid are:
Therefore, the total surface area (excluding one base) is:
[tex]SA = \pi \cdot 2^2+2\pi \cdot 2 \cdot 7\\\\SA = 4\pi +28\pi \\\\SA=32\pi\; \sf in^2[/tex]
[tex]\dotfill[/tex]
Percent
To determine what percent of the total surface area is blue, divide the surface area of the blue part by the total surface area:
[tex]\textsf{Percent}=\dfrac{8\pi}{32\pi}\\\\\\\textsf{Percent}=\dfrac{1}{4}\\\\\\\textsf{Percent}=0.25\\\\\\\textsf{Percent}=25\%[/tex]
Therefore, 25% of the total surface area is blue.
