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Question

The wedge is one-eighth of the wheel of cheese

(a) Find the surface area of the cheese before it is cut.

(b) Find the surface area of the remaining cheese after the wedge is removed. Did the surface area increase, decrease, or remain the same?


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Solution

Hint:

Step 1: (a) The surface area of the cheese before removing the wedge =2πr2+2πrh

Surface area =2×3.14×3×3+2×3.14×3×1

Surface area =(56.52+18.84)sq.in

Surface area =75.36sq.in

Step 2: (b) The surface area of wedge =18 of wheel of cheese

The surface area of wheel of cheese after removing wedge =78×75.36sq.in+2×3×1sq.in

The surface area of wheel of cheese after removing =65.94sq.in+6sq.in

The surface area of wheel of cheese after removing wedge =71.94sq.inch

Final answer: The surface area of wheel of cheese decreases after removing wedge


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