Anita made a wax model of a rolling pin of diameter 6 cm. The rolling pin was shaped like a right circular cylinder with a right circular cone at each end as shown below. A rolling pin shaped as a cylinder with conical ends. The length of the cylindrical part is 9 cm, the slant height of each cone is 4 cm and the diameter of the rolling pin is 6 cm. What was the total surface area of the rolling pin? Using complete sentences, describe the steps you used to calculate the surface area.

Question

Anita made a wax model of a rolling pin of diameter 6 cm. The rolling pin was shaped like a right circular cylinder with a right circular cone at each end as shown below.  A rolling pin shaped as a cylinder with conical ends. The length of the cylindrical part is 9 cm, the slant height of each cone is 4 cm and the diameter of the rolling pin is 6 cm.  What was the total surface area of the rolling pin? Using complete sentences, describe the steps you used to calculate the surface area.

hero · Answer

And what exactly is the trouble you're having with this?

hero · Answer

All you have to do is find the surface area of each part separately, then subtract off the surface areas that are not part of the total surface area of the rolling pin.

hero · Answer

You know the formulas for surface area of cylinder and surface area of a cone, right?

anonymous · Answer

yea

hero · Answer

Okay, so...what have you done so far?

anonymous · Answer

okay hold on, 
so that area of a cylinder is 2 pi r squared. So part of it would be 2*3.14*3squared right

anonymous · Answer

and then i don't remember where to go to from there

hero · Answer

Well, there's more at play here than just a cylinder. We have a right circular cylinder and a 2 right circular cones on the ends of that cylinder. We have to find the total surface area of that. Right off the bat, the first thing I notice is that the total surface area will be less than the sum of the individual surface areas simply because those three objects have been sort of merged into one object.

hero · Answer

I think the best approach to this would be to find the surface area of each individual object, then start subtracting the circular areas of each one. The circular surface areas are not included in the total surface area. So you can calculate the surface area of each object, then subtract $4\pi r $ from each one.

anonymous · Answer

ohh okay..so how would i start it

hero · Answer

Well, 

1. Find the surface area of the right circular cylinder. Subtract $4\pi r$ from that. 
2. Find the surface area of the right circular cone. Multiply that by 2. Then subtract $4\pi r$ from that. 
3. Add the remaining surface areas of steps 1 and 2 together to get the total surface area of the rolling pin.

anonymous · Answer

okay thanks (:

hero · Answer

Let me know what you get