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?

Answer 1

Hint:

Step 1: (a) The surface area of the cheese before removing the wedge $=2{\mathrm{\pi r}}^2+2\mathrm{\pi rh}$

Surface area $=2\times 3.14\times 3\times 3+2\times 3.14\times 3\times 1$

Surface area $=(56.52+18.84)sq.in$

Surface area $=75.36sq.in$

Step 2: (b) The surface area of wedge $=\frac{1}{8}$ of wheel of cheese

The surface area of wheel of cheese after removing wedge $=\frac{7}{8}\times 75.36sq.in+2\times 3\times 1sq.in$

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