A can of olives has a diameter of 6 inches and a height of 4 inches. How many square inches of paper will be needed the label on the outside of the can? Use 3.14 for p (INR)
To find the surface area of the can, we need to calculate the area of the curved surface (the lateral surface area) and the area of the circular top and bottom.
The curved surface area can be calculated using the formula:
Lateral Surface Area = circumference × height
The circumference of the can is equal to the perimeter of the circular top/bottom, which can be calculated using the formula:
Circumference = diameter × π
Given that the diameter of the can is 6 inches and π is 3.14, we can calculate the circumference:
Circumference = 6 inches × 3.14 = 18.84 inches
Now, we can calculate the lateral surface area:
Lateral Surface Area = 18.84 inches × 4 inches = 75.36 square inches
The area of the circular top/bottom can be calculated using the formula:
Circular Area = π × (radius)^2
The radius is equal to half the diameter, so in this case, it is 6 inches / 2 = 3 inches.
The circular area can be calculated:
Circular Area = 3.14 × (3 inches)^2 = 28.26 square inches
Since there are two circular tops/bottoms, the total area for both is 2 × 28.26 = 56.52 square inches.
Adding the lateral surface area and the area of the circular tops/bottoms, we get:
Total Surface Area = 75.36 square inches + 56.52 square inches = 131.88 square inches
Therefore, approximately 131.88 square inches of paper will be needed for the label on the outside of the can.