The cut wedge represents one-eighth of the cheese. A. Find the surface area of the cheese before it is cut in terms of π ,rounded to the nearest whole number, and as a decimal, round to the nearest tenth. The surface area of the cheese before it is cut is π , or about in.2 2 . B. Find the surface area of the remaining cheese after the wedge is removed. Round the estimated portion of the answer to the nearest whole number. The surface area of the remaining cheese after the wedge is removed is about square inches. Question 2 Did the surface area increase, decrease, or remain the same? Response - correct The surface area decreased.

A. The surface area of the cheese is 24·π in.² or 75.40 in.²

B. The surface area of the remaining cheese after the wedge is removed is about 72 in.²

2. The surface area decreased

Step-by-step explanation:

From the figure attached to a similar question, we have;

Radius, r of cheese = 3 in.

Height, h of the cheese = 1 in.

A. The surface area of the cheese is equal to the area of two circles, one on top and the other underneath added to the surface area of the sides which is equivalent to the surface area of a cylinder given by the relation

Surface area of the cheese = 2×π×r² + 2×π×r×h

∴ Surface area of the cheese = 2×π×3² + 2×π×3×1 = 24·π in.²

Surface area of the cheese = 24·π = 75.398 ≈ 75.40 in.² to the nearest 10th

B. The surface area of the remaining cheese after the wedge is removed is found by first subtracting the cut wedge from the total surface area as follow

Outer surface area of cut wedge = 24·π÷8 = 3·π

New outer surface area = Total surface area - Removed outer surface area

∴ New outer surface area = 24·π - 3·π = 21·π

New total surface area = New outer surface area + Area of newly exposed segment

Area of newly exposed segment = 3 × 1 × 2 = 6 in.²

∴ New total surface area = (21·π + 6) in.² = 71.9734 in.² ≈ 72 in.²

The surface area of the remaining cheese after the wedge is removed is about 72 in.²

2. The surface area decreased.

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step-by-step explanation: