Question

The wedge is one-eighth of the wheel of cheese. A cylindrical-shaped wheel of cheese has a radius of 3 inches and height of 1 inch. A wedge of cheese is sliced from the whole. a. Find the surface area of the cheese before it is cut, round to the nearest hundredth. The surface area of the cheese before it is cut is in. $^2$ . b. Find the surface area of the remaining cheese after the wedge is removed, round to the nearest hundredth. 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

Answer 1

The surface area of the cheese before it is cut is approximately 75.4 square inches. After the wedge is removed, the surface area of the remaining cheese is approximately 149.2 square inches.

Step-by-step explanation:

To find the surface area of the cheese before it is cut, we need to find the surface area of a cylinder. The formula for the surface area of a cylinder is 2πrh + 2πr^2, where r is the radius and h is the height. In this case, the radius is 3 inches and the height is 1 inch. Plugging these values into the formula, we get:

Surface Area = 2π(3)(1) + 2π(3)^2 = 6π + 18π = 24π ≈ 75.4 square inches.

To find the surface area of the remaining cheese after the wedge is removed, we need to subtract the surface area of the wedge from the surface area of the whole cheese. The formula for the surface area of a wedge is 2πrh, where r is the radius and h is the height of the wedge. Since the wedge is one-eighth of the whole cheese, the height of the wedge is 1/8 of the height of the whole cheese. Plugging in the values, we get:

Wedge Surface Area = 2π(3)(1/8) = π/2. The surface area of the remaining cheese is the surface area of the whole cheese minus the surface area of the wedge:

Remaining Surface Area = 24π - π/2 = (48/2)π - (1/2)π = 47.5π ≈ 149.2 square inches.

Answer 2

1. a. 75.39 in² b. 65.97 in²

2. Decreased

Step-by-step explanation:

1.

a. Find the surface area of the cheese before it is cut, round to the nearest hundredth.

Since the cheese is a cylinder with radius, r = 3 inches and height, h = 1 inch, its tital surface area, A = 2πr(r + h)

Substituting the values of the variables into the equation, we have

A = 2πr(r + h)

A = 2π(3 in)(3 in + 1 in)

A = (6π in)(4 in)

A = 24π in²

A = 75.39 in²

b. Find the surface area of the remaining cheese after the wedge is removed, round to the nearest hundredth.

Since the area of the wedge, A' is one-eight the area of the cheese, A

A'= A/8

= 75.39 in²/8

= 9.42 in²

The area of the remaining cheese is thus, area of cheese - area of wedge = A - A' = 75.39 in² - 9.42 in² = 65.97 in²

Question 2 - Did the surface area increase, decrease, or remain the same

Since the area of the remaining cheese, A' = 65.97 in² < A = 75.39 in², area of original cheese, the surface area decreased.