Final answer:
To calculate the density of a cylinder-shaped soda can, we find the volume using the formula πr2h and then divide the mass of the can, which is 40 g, by this volume. However, the value obtained does not match any of the provided options, indicating a potential error.
Step-by-step explanation:
To find the density of the soda can, we need to calculate its volume and then use the formula for density, which is mass divided by volume. The formula for the volume of a cylinder (which is the shape of the soda can) is πr2h, where r is the radius, and h is the height.
The radius of the soda can is 3.25 cm, and the height is 12.2 cm. So, the volume V is:
V = π(3.25 cm)2(12.2 cm) = π(10.5625 cm2)(12.2 cm) = π(128.8625 cm3)
Once we calculate this value, we then find the density using the mass of the can, which is 40 g.
Density = mass / volume = 40 g / π(128.8625 cm3)
To get the numerical value, we approximate π as 3.1416 and calculate:
Density ≈ 40 g / (3.1416 × 128.8625 cm3) = 40 g / 405.363 cm3 ≈ 0.0987 g/cm3
None of the provided options (a-d) match this calculated value, suggesting there might have been an error in the question or the answer choices.