Answer:
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.
