Titanium is used in airplane bodies because it is strong and light. It has a density of 4.55 g/cm^3. If a cylinder of titanium is 7.75 cm long and has a mass of 153.2 g, calculate the diameter of the cylinder. (V=pi*r^2*h, where V is the volume of the cylinder, r is the radius, and h is the height.)
To find the diameter of the cylinder, we need to first find the volume of the cylinder using the given mass and density.
Step 1: Calculate the volume of the cylinder using the formula V = π * r^2 * h, where V is the volume, r is the radius, and h is the height.
Given: density (ρ) = 4.55 g/cm^3, length (h) = 7.75 cm, mass (m) = 153.2 g
Step 2: Rearrange the formula to solve for the radius (r).
V = π * r^2 * h
Since the density (ρ) = m / V, we have:
V = m / ρ
Therefore, we can rewrite the formula:
m / ρ = π * r^2 * h
Dividing both sides of the equation by π * h:
(m / ρ) / (π * h) = r^2
Taking the square root of both sides:
r = √((m / ρ) / (π * h))
Step 3: Substitute the given values into the formula to calculate the radius.
r = √((m / ρ) / (π * h))
r = √((153.2 g / 4.55 g/cm^3) / (π * 7.75 cm))
r = √(33.68 cm^3 / (3.14 * 7.75 cm))
r ≈ √(4.273)
r ≈ 2.07 cm
Step 4: Calculate the diameter by multiplying the radius by 2.
d = 2 * r
d ≈ 2 * 2.07 cm
d ≈ 4.14 cm
Therefore, the diameter of the cylinder is approximately 4.14 cm.
To calculate the diameter of the titanium cylinder, we first need to find its volume using the formula V = π * r^2 * h, where V is the volume, r is the radius, and h is the height.
Given that the density of titanium is 4.55 g/cm^3, we can calculate the mass of the cylinder by multiplying the density by its volume:
Mass = Density * Volume
153.2 g = (4.55 g/cm^3) * Volume
Rearranging the equation to solve for the volume, we have:
Volume = Mass / Density
Volume = 153.2 g / (4.55 g/cm^3)
Volume = 33.6 cm^3
Now, we can substitute the given values into the volume formula:
33.6 cm^3 = π * r^2 * 7.75 cm
Rearranging the equation to solve for the radius, we have:
r^2 = (33.6 cm^3) / (π * 7.75 cm)
r^2 ≈ 1.41 cm^2
Taking the square root of both sides, we can find the value of r:
r ≈ √(1.41 cm^2)
r ≈ 1.19 cm
Finally, we can calculate the diameter by multiplying the radius by 2:
Diameter = 2 * r
Diameter ≈ 2 * 1.19 cm
Diameter ≈ 2.38 cm
Therefore, the diameter of the titanium cylinder is approximately 2.38 cm.
volume = mass/density
Solve for volume.
Volume = pi*r^2h.
Solve for r, then diameter = 2r.