The original Aunt Emma's Root Beer can was 13.9 cm high. The new can is 2.6 cm shorter. The new can has a diameter of 7.0 cm. What is the volume of the new​ can? Use pi almost equals 3.14.

Question

The volume of the new can is

Answer 1

To find the volume of the new can, we first need to determine its height and then apply the formula for the volume of a cylinder.

1. Determine the height of the new can: The original can's height is 13.9 cm and the new can is 2.6 cm shorter: \[ \text{Height of new can} = 13.9 , \text{cm} - 2.6 , \text{cm} = 11.3 , \text{cm} \]

2. Use the formula for the volume of a cylinder: The formula for the volume \( V \) of a cylinder is given by: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.

   Since the diameter of the new can is 7.0 cm, we can find the radius: \[ r = \frac{\text{diameter}}{2} = \frac{7.0 , \text{cm}}{2} = 3.5 , \text{cm} \]

3. Substitute the values into the formula: Now we can calculate the volume: \[ V = 3.14 \times (3.5 , \text{cm})^2 \times 11.3 , \text{cm} \] First, calculate \( (3.5 , \text{cm})^2 \): \[ (3.5 , \text{cm})^2 = 12.25 , \text{cm}^2 \]

   Next, substitute back into the volume formula: \[ V = 3.14 \times 12.25 , \text{cm}^2 \times 11.3 , \text{cm} \]

   Calculate: \[ V = 3.14 \times 12.25 = 38.405 , \text{cm}^2 \] Then multiply by the height: \[ V = 38.405 , \text{cm}^2 \times 11.3 , \text{cm} \approx 434.78 , \text{cm}^3 \]

Conclusion: The volume of the new can is approximately 434.78 cm³.