Bot GPT 4-o mini To find the surface area that needs to be labeled on the outside of the can of olives, we need to calculate the lateral surface area of the cylinder and the area of the top and bottom circles.
The formula for the lateral surface area (A_lateral) of a cylinder is:
\[ A_{lateral} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height. The radius \( r \) is half of the diameter.
Given:
- Diameter = 6 inches
- Radius \( r = \frac{6}{2} = 3 \) inches
- Height \( h = 4 \) inches
Using the lateral surface area formula:
\[ A_{lateral} = 2 \times 3.14 \times 3 \times 4 \]
Calculating this:
\[ A_{lateral} = 2 \times 3.14 \times 3 \times 4 = 2 \times 3.14 \times 12 = 2 \times 37.68 = 75.36 \text{ square inches} \]
Next, we calculate the area of the top and bottom circles. The formula for the area of a circle is:
\[ A_{circle} = \pi r^2 \]
So the area for one circle:
\[ A_{circle} = 3.14 \times 3^2 = 3.14 \times 9 = 28.26 \text{ square inches} \]
Since there are two circles (top and bottom):
\[ A_{top\ and\ bottom} = 2 \times 28.26 = 56.52 \text{ square inches} \]
Now, we combine the lateral area and the area of the circles to find the total surface area:
\[ A_{total} = A_{lateral} + A_{top\ and\ bottom} \] \[ A_{total} = 75.36 + 56.52 = 131.88 \text{ square inches} \]
Thus, the total surface area needed for the label on the outside of the can is 131.88 square inches.
Response: 131.88
1 answer