12C Questions

[calcguy1350]

Geometric Modeling?:12C-37 A 36-yd roll of scotch tape is spooled onto a roller. The roller is 3.5 cm in diameter, and the tape on a new roll has a 6cm diameter. What is the tape diameter when the roll is 65% used? Answer: 4.53cm

Physics: 12C-38 A motorcycle dare devil rides his motorcycle up a [unparseable or potentially dangerous latex formula] ramp at 55 mph. The ramp was built using 10 sheets of 8-ft long plywood. What is the horizontal distance from the end of the ramp to the spot on the ground where the dare devil lands? Answer: 183 ft.

Scaling: 12C-46 A dozen donuts requires 14 tablespoons of glaze to cover them completely. How much glaze would be needed if the same amount of dough was used to make 2 large donuts? Answer: 7.70 tbsp

Help me please. Thanks.

[rcoker7]

12C-37: We can imagine the spool of tape as a continuous area of tape surrounding the inner section. You just need to find the area the tape covers originally, multiply that by .35 and find the new diameter.
area(original)=pi*(3^2-1.75^2)=18.65.
area(new)=18.65*.35=6.53.
This area = pi*(r^2-1.75^2). r=2.27. d=2r=4.53.

[88bobcat]

[Shawn]

46) Scaling:
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
This is somewhat of a tricky problem, because you would think at first that it is surface area. The changing factor is the volume though. I scaled to 1, but by replacing this by 14 you could eliminate a step.

[calcguy1350]

I was really lost in these, NOW I get them. Thank you very much Shawn, Bobcat, and Ross, your help is greatly appreciated!

[rcoker7]