Answer: The height of the silver cylinder is approximately 17.56 cm.
Step-by-step explanation:
To find the height of the silver cylinder, you can use the formula for the volume of a cylinder:
Volume = π * r² * h
Where:
π (pi) is approximately 3.14159.
r is the radius of the cylinder.
h is the height of the cylinder.
You have the mass of the silver cylinder (145g) and its density (10.5 g/cm³). To calculate the volume, you can use the formula for density:
Density = Mass / Volume
Rearrange this formula to solve for volume:
Volume = Mass / Density
Now, plug in the values:
Volume = 145g / 10.5 g/cm³ = 13.81 cm³
Now, you know the volume of the cylinder is 13.81 cm³. You also have the radius, which is 0.5 cm. Plug these values into the formula for the volume of a cylinder:
13.81 cm³ = π * (0.5 cm)² * h
Now, solve for h (the height):
h = 13.81 cm³ / (π * (0.5 cm)²)
h = 13.81 cm³ / (π * 0.25 cm²)
h = 13.81 cm³ / (0.7854 cm²)
h ≈ 17.56 cm
So, the height of the silver cylinder is approximately 17.56 cm.