Questions: Find the volume of a beverage can that has a height of 8.5 in. and a diameter of 3.6 in. Use 3.14 as an approximation for π. The volume of the can is (Type an integer or a decimal rounded to the nearest hundredth as needed.)

Solution Steps

To find the volume of a cylindrical beverage can, we use the formula for the volume of a cylinder: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Given the diameter, we can find the radius by dividing the diameter by 2. Then, we substitute the values into the formula to calculate the volume.

Given the diameter \( d = 3.6 \) in, we find the radius \( r \) using the formula: \[ r = \frac{d}{2} = \frac{3.6}{2} = 1.8 \text{ in} \]

The volume \( V \) of a cylinder is calculated using the formula: \[ V = \pi r^2 h \] Substituting the values \( \pi \approx 3.14 \), \( r = 1.8 \) in, and \( h = 8.5 \) in, we have: \[ V = 3.14 \times (1.8)^2 \times 8.5 \]

Calculating \( (1.8)^2 \): \[ (1.8)^2 = 3.24 \] Now substituting back into the volume formula: \[ V = 3.14 \times 3.24 \times 8.5 \] Calculating this gives: \[ V \approx 86.4756 \text{ in}^3 \] Rounding to the nearest hundredth, we find: \[ V \approx 86.48 \text{ in}^3 \]

Final Answer