A cylindrical carton of oatmeal with radius of 3.5 in. is 9 in tall. If all surfaces except the top are made of cardboard , how much cardboard is used to make the oatmael carton. Round your answer to the nearest square inch
I don't understand how to do this
197.8
Right.
Multiply:
2 * 3.14 * 3.5 * 9 = ?
Bottom:
A = pi * r^2
A = 3.14 * 3.5^2
A = 38.465 square inches
Sides:
A = 2 * pi * r * h
Add the two areas together and round.
To find the amount of cardboard used to make the oatmeal carton, we need to calculate the total surface area of the carton excluding the top.
The total surface area of a cylinder consists of three parts: the curved surface area (lateral area), the top circular base, and the bottom circular base.
1. Curved Surface Area (Lateral Area):
The curved surface area of a cylinder can be calculated by multiplying the height of the cylinder by the circumference of its circular base. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. So, the curved surface area of the oatmeal carton is given by A_curved = 2πrh.
In this case, the radius (r) is 3.5 inches, and the height (h) is 9 inches. Plugging in these values, we get:
A_curved = 2 * π * 3.5 * 9 = 63π square inches.
2. Circular Base:
The total area of the circular base is given by the formula A_base = πr^2, where r is the radius of the circle. Since we are excluding the top, we need to calculate the area of only one base.
Using the given radius, we have:
A_base = π * (3.5)^2 = 12.25π square inches.
3. Total Surface Area (excluding top):
The total surface area of the oatmeal carton, excluding the top, is the sum of the curved surface area and the area of one base. So, A_total = A_curved + A_base.
A_total = 63π + 12.25π = 75.25π square inches.
Now, to get the answer rounded to the nearest square inch, we need to calculate the approximate value of π and perform the rounding.
Using the value π ≈ 3.14159, we can substitute it into the equation:
A_total ≈ 75.25 * 3.14159 ≈ 236.89 square inches.
Rounding the result to the nearest square inch, the amount of cardboard used to make the oatmeal carton is approximately 237 square inches.