An oatmeal box is shaped like a cylinder with 2 inch radius and 9 inch height. Use a net to find the surface area S of the oatmeal box to the nearest tenth. Then find the number of square feet of cardboard needed for 1,500 oatmeal boxes. Round your answer to the nearest whole number.
THANK YOU!!
As = 2pir^2 + 2pi*r*h =
6.28*2^2 + 6.28*2*9 = 138.2 In^2.
138.2In^2 * 1Ft^2/144In^2 = 0.959
Ft^2.
0.959Ft^2/box * 1500boxes = 1439.2 Ft^2. of cardboard.
To find the surface area of the oatmeal box, we need to calculate the areas of the individual faces and add them together.
First, let's find the area of the circular top and bottom of the cylinder. The formula for the area of a circle is A = πr^2, where r is the radius. In this case, the radius is given as 2 inches. So, the area of each circular face is:
A_circle = π * (2 inches)^2
To find the area of the curved surface, we need to calculate the lateral area of the cylinder. The formula for the lateral area of a cylinder is A_lateral = 2πrh, where r is the radius and h is the height. In this case, the radius is 2 inches and the height is 9 inches. So, the area of the curved surface is:
A_lateral = 2π * (2 inches) * (9 inches)
Now, let's calculate the total surface area by adding up all the areas:
S = 2 * A_circle + A_lateral
Substituting the values we calculated:
S = 2 * (π * (2 inches)^2) + (2π * (2 inches) * (9 inches))
To get the answer to the question, simply plug these values into a calculator or use the value of π as approximately 3.14.
Now, to find the number of square feet of cardboard needed for 1,500 oatmeal boxes, we need to multiply the surface area of one box by the total number of boxes. Once we have the surface area, we can convert it to square feet.
Once you have the surface area of one oatmeal box, multiply it by 1,500 to get the total surface area of 1,500 boxes.
Finally, since the surface area is given in square inches, you need to convert it to square feet by dividing by 144 (since there are 144 square inches in a square foot). Round the final answer to the nearest whole number.
Remember to use the appropriate value for π (either 3.14 or a more precise value) in your calculations.