Answer and Step-by-step explanation:
For question 1:
The net for the cylindrical candy container has a rectangle with a height of 0.7 inches and a length of the circumference of the circular bases, which is π(1.6) inches. The area of the rectangle is (0.7)(π(1.6)) = 1.12π square inches. The two circular bases each have an area of (1/2)π(0.8)^2 = 0.4π square inches. The total surface area covered by the plastic wrap is the sum of the area of the rectangle and the two circular bases, which is 1.12π + 0.4π + 0.4π = 1.92π square inches. Therefore, the answer is option A: 1.84π square inches (rounded to two decimal places).
For question 2:
The surface area of a cylinder is given by the formula 2πr(r+h), where r is the radius of the circular base and h is the height of the cylinder. Substituting the given values, we get 2π(5)(5+4) = 2π(5)(9) = 90π square inches. Therefore, the answer is option C: 282.6 in2.
For question 3:
The correct formula for the surface area of a cylinder is SA = 2πrh + 2πr^2, where r is the radius of the circular base and h is the height of the cylinder. The given cylinder has a diameter of 3.2 feet and a height of 3.8 feet, so its radius is 1.6 feet. Substituting these values into the formula, we get SA = 2π(1.6)(3.8) + 2π(1.6)^2 = 12.032π square feet. Therefore, the answer is option A: SA = 2π(1.6)2 + 3.2π(3.8) square feet.
For question 4:
The surface area of the circular bottom of the cake is πr^2, where r is the radius of the circular bottom. Substituting the given values, we get π(15)^2 = 225π square centimeters. The lateral surface area of the cake (everything but the circular bottom) is given by the formula 2πrh, where r is the radius of the circular bottom and h is the height of the cake. Substituting the given values, we get 2π(15)(12) = 360π square centimeters. Therefore, the total surface area of the cake is 225π + 360π = 585π square centimeters. Rounding to the nearest square centimeter, the answer is option B: 585 cm2.
For question 5:
The lateral surface area of the wheel of cheese (everything except the circular top and bottom) is given by the formula 2πrh, where r is the radius of the circular base and h is the height of the cylinder. Substituting the given values, we get 2(22/7)(20)(18) = 2520 square centimeters. The label covers the lateral surface area of the wheel, so it covers 2520 square centimeters. Therefore, the answer is option B: 15,840/7 square centimeters.
For question 6:
The surface area of a cylinder is given by the formula SA = 2πr^2 + 2πrh, where r is the radius and h is the height. Since the diameter is 6 inches, the radius is half of that, or 3 inches.
We are given that the surface area of the tub is 183.69 square inches, so we can write the equation:
183.69 = 2π(3^2) + 2π(3)h
Simplifying and solving for h, we get:
183.69 = 18π + 6πh
165.69 = 6πh
h = 165.69/(6π)
h ≈ 4.45 inches
Therefore, the height of the cylindrical gallon tub is approximately 4.45 inches. Rounded to the nearest hundredth, the answer is 4.5 inches. So the correct answer is B. 4.5 inches.
Question 7:
The surface area of a cylinder is given by the formula SA = 2πr(r+h), where r is the radius and h is the height of the cylinder.
Substituting the given values, we get:
SA = 2π(1.25)(1.25+2.75)
SA = 2π(1.25)(4)
SA = 10π
Therefore, the exact surface area of the cylinder in terms of π is 10π square centimeters. The answer is option B.