Answer:
C
Step-by-step explanation:
We can find the surface area of the dumbbell by adding the surface areas of each part. We have two equal round ends of the dumbbell to count and the skinnier inside. Each is a cylinder and each can be found by finding the area of the base (times 2 for two bases) and adding it to the circumference times the height.
[tex]2(\pi r^{2} )+(\pi d)h[/tex]
Dumbbell Ends
There are two ends and so we will count this measurement twice. The diameter is 12.5. The radius is half of this and is 6.25. The height is 8.
[tex]2(\pi r^{2} )+(\pi d)h[/tex]
[tex]2(\pi (6.25)^{2} )+(\pi 12.5)8[/tex]
[tex]2(\pi 39.0625 )+(\pi 100[/tex]
245.4369+314= 559.43
But we must count is twice, so 559.43(2)=1118.87 cm squared.
Dumbbell Middle
The diameter is 2.50. Radius is 1.25. The height is 10.5. The ends actually don't show because they are attached. So we will only calculate the second part and add it to the other.
[tex](\pi 2.5)10.5[/tex]=82.47
82.47+1118.87=1201.33 cm squared.
Why is this too large? Why isn't it an answer choice? Because the ends of the middle don't show, they also take up that much area on other side. They are not part of the surface area and they make it smaller. So we will subtract that area now.
[tex]2(\pi 1.25^{2} )[/tex]=9.817
1201.33-9.817=1191.84 cm squared.
