Math

QuestionA circular cake weighs 12 pounds. If wedges with a 6060^{\circ} angle are cut, what is the weight of each wedge?

Studdy Solution

STEP 1

Assumptions1. The cake is a circle and it's uniformly distributed, meaning each part of the cake weighs the same per unit area. . The cake weighs12 pounds.
3. The baker wants to cut wedges with a 6060^{\circ} angle from the center of the cake.
4. A full circle has 360360^{\circ}.

STEP 2

First, we need to find out how many wedges of 6060^{\circ} can be cut from the cake. We can do this by dividing the total degrees in a circle by the degrees of each wedge.
Numberofwedges=Totaldegreesinacircle/DegreesperwedgeNumber\, of\, wedges = Total\, degrees\, in\, a\, circle / Degrees\, per\, wedge

STEP 3

Now, plug in the given values for the total degrees in a circle and degrees per wedge to calculate the number of wedges.
Numberofwedges=360/60Number\, of\, wedges =360^{\circ} /60^{\circ}

STEP 4

Calculate the number of wedges.
Numberofwedges=360/60=6Number\, of\, wedges =360^{\circ} /60^{\circ} =6

STEP 5

Now that we have the number of wedges, we can find the weight of each wedge. This can be done by dividing the total weight of the cake by the number of wedges.
Weightperwedge=Totalweight/NumberofwedgesWeight\, per\, wedge = Total\, weight / Number\, of\, wedges

STEP 6

Plug in the values for the total weight and the number of wedges to calculate the weight per wedge.
Weightperwedge=12pounds/6Weight\, per\, wedge =12\, pounds /6

STEP 7

Calculate the weight per wedge.
Weightperwedge=12pounds/6=2poundsWeight\, per\, wedge =12\, pounds /6 =2\, poundsEach wedge will weigh2 pounds.

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