If a cylindrical container's height is 8 inches and radius is 2.5 inches, what is the area of a label that is ¾ the height of the cylinder and overlaps by 1 inch?

If a cylindrical container's height is 8 inches and radius is 2.5 inches, what is the area of a label that is ¾ the height of the cylinder and overlaps by 1 inch?

• A. 90 square inches
• B. 93 square inches
• C. 95 square inches
• D. 100 square inches

Answer: (B)

To find the area of the label on the cylindrical container, we first need to determine the relevant dimensions of the label. The height of the cylinder is 8 inches, so the height of the label, which is three-quarters of the cylinder's height, is calculated as follows: \[ \text{Height of the label} = \frac{3}{4} \times 8 = 6 \text{ inches} \] Next, we consider the overlap. The label overlaps the cylinder by 1 inch at the top and bottom, effectively reducing the actual visible height of the label. Therefore, the height that contributes to the label area is: \[ \text{Effective height of the label} = \text{Height of the label} - 2 \times \text{overlap} = 6 - 2 \times 1 = 6 - 2 = 4 \text{ inches} \] Now, we need to calculate the circumference of the base of the cylinder to find the width of the label. The formula for the circumference \( C \) of a cylinder is given by: \[ C = 2\pi r \] Where \( r \) is the radius.

To find the area of the label on the cylindrical container, we first need to determine the relevant dimensions of the label.

The height of the cylinder is 8 inches, so the height of the label, which is three-quarters of the cylinder's height, is calculated as follows:

[

\text{Height of the label} = \frac{3}{4} \times 8 = 6 \text{ inches}

]

Next, we consider the overlap. The label overlaps the cylinder by 1 inch at the top and bottom, effectively reducing the actual visible height of the label. Therefore, the height that contributes to the label area is:

[

\text{Effective height of the label} = \text{Height of the label} - 2 \times \text{overlap} = 6 - 2 \times 1 = 6 - 2 = 4 \text{ inches}

]

Now, we need to calculate the circumference of the base of the cylinder to find the width of the label. The formula for the circumference ( C ) of a cylinder is given by:

[

C = 2\pi r

]

Where ( r ) is the radius.