Bot GPT 4-o mini To find out how much paper will be needed for the label on the outside of the can, we need to calculate the surface area of the cylinder (the can of olives).
The formula for the surface area \( A \) of a cylinder is:
\[ A = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately \( 3.14 \).
For the can of olives:
- The diameter is \( 6 \) inches, so the radius \( r \) is \( \frac{6}{2} = 3 \) inches.
- The height \( h \) is \( 4 \) inches.
Now we can plug in the values into the surface area formula:
- Calculate the area of the two circular bases:
\[ 2\pi r^2 = 2 \times 3.14 \times (3^2) = 2 \times 3.14 \times 9 = 56.52 \text{ square inches} \]
- Calculate the lateral surface area:
\[ 2\pi rh = 2 \times 3.14 \times 3 \times 4 = 2 \times 3.14 \times 12 = 75.36 \text{ square inches} \]
- Now add the areas of the bases and the lateral surface area to find the total surface area:
\[ A = 56.52 + 75.36 = 131.88 \text{ square inches} \]
Thus, the total area of paper needed for the label on the outside of the can is 131.88 square inches.
The correct response from the choices provided is: 131.88
1 answer