Find the mass of a hollow sphere of lead,with external diameter 10 cm and thickness 2 mm,if 1 cm^3 of lead weighs 11.4 gm.
Why did the lead sphere go on a diet? Because it wanted to look thin from the outside! Okay, let's calculate its mass now.
To find the mass of the hollow sphere, let's first determine its volume. The external diameter is given as 10 cm, so the radius would be half of that, which is 5 cm. The thickness is given as 2 mm, which means there's an inner sphere with a radius of 5 cm - 2 mm = 4.8 cm.
The volume of the hollow sphere can be calculated using the formula:
Volume = (4/3) * π * (r_external^3 - r_internal^3)
Let's plug in the values and calculate:
Volume = (4/3) * π * ((5 cm)^3 - (4.8 cm)^3)
Now that we have the volume, we can find the mass by multiplying it with the density of lead:
Mass = Volume * Density
Since 1 cm^3 of lead weighs 11.4 gm, we can substitute that value:
Mass = Volume * 11.4 gm/cm^3
There you go! Calculate the volume and multiply it by 11.4 to find the mass of the lead hollow sphere. Good luck, and don't forget to keep an eye on the sphere's waistline!
To find the mass of a hollow sphere of lead, we need to calculate the volume and multiply it by the density of lead.
Step 1: Calculate the internal diameter of the hollow sphere.
The external diameter is given as 10 cm, and the thickness is given as 2 mm. The internal diameter can be obtained by subtracting twice the thickness from the external diameter.
Internal diameter = external diameter - 2 * thickness
Internal diameter = 10 cm - 2 * 2 mm
Internal diameter = 10 cm - 4 mm
Internal diameter = 10 cm - 0.4 cm = 9.6 cm
Step 2: Calculate the radius of the hollow sphere.
The radius of the sphere is half of the internal diameter.
Radius = 9.6 cm / 2 = 4.8 cm
Step 3: Calculate the volume of the hollow sphere.
Volume of a hollow sphere = (4/3) * π * (R^3 - r^3), where R is the external radius and r is the internal radius.
We need to convert the radius from cm to meters in order to use the formula.
Radius in meters = 4.8 cm * (1 m / 100 cm) = 0.048 m
Volume of the hollow sphere = (4/3) * π * ((0.048)^3 - (0.046)^3)
Volume of the hollow sphere = (4/3) * π * (0.0115776 - 0.0108596)
Volume of the hollow sphere = (4/3) * π * 0.000718
Volume of the hollow sphere ≈ 0.003018 m^3
Step 4: Calculate the mass of the hollow sphere.
The density of lead is given as 11.4 gm/cm^3. We need to convert the volume from m^3 to cm^3 in order to multiply it by the density.
Volume in cm^3 = 0.003018 m^3 * (1 * 10^6 cm^3 / 1 m^3)
Volume in cm^3 = 3018 cm^3
Mass of the hollow sphere = Volume in cm^3 * Density of lead
Mass of the hollow sphere = 3018 cm^3 * 11.4 gm/cm^3
Mass of the hollow sphere ≈ 34,450.52 gm or 34.45 kg
Therefore, the mass of the hollow sphere of lead is approximately 34.45 kg.
To find the mass of the hollow sphere of lead, you need to calculate the volume of the lead used and then multiply it by the weight of 1 cm^3 of lead.
1. Calculate the internal radius:
The external diameter of the sphere is given as 10 cm, and the thickness is 2 mm. To find the internal diameter, subtract twice the thickness from the external diameter:
Internal Diameter = External Diameter - 2 * Thickness
Internal Diameter = 10 cm - 2 * 0.2 cm
Internal Diameter = 9.6 cm
Divide the internal diameter by 2 to find the internal radius:
Internal Radius = Internal Diameter / 2
Internal Radius = 9.6 cm / 2
Internal Radius = 4.8 cm
2. Calculate the volume of the lead sphere:
The volume of a hollow sphere is given by the formula:
Volume = (4/3) * π * (R^3 - r^3)
Where R is the external radius and r is the internal radius.
External Radius = External Diameter / 2
External Radius = 10 cm / 2
External Radius = 5 cm
Volume = (4/3) * π * (5^3 - 4.8^3)
Volume = (4/3) * 3.14159 * (125 - 110.592)
Volume = 4.18879 * 14.40841
Volume = 60.438
Volume = 60.438 cm^3
3. Calculate the mass of the lead sphere:
Now, multiply the volume of the lead sphere by the weight of 1 cm^3 of lead:
Mass = Volume * Weight of 1 cm^3 of lead
Mass = 60.438 cm^3 * 11.4 gm/cm^3
Mass ≈ 689.998 gm
Therefore, the mass of the hollow sphere of lead is approximately 689.998 grams.
Multiply the volume by the density. The volume is the difference between that of a 5.0 cm radius sphere and a 4.8 cm radius sphere.
M = (4/3)*pi[5.0^2 - 4.8^2](cm^3)*11.4 g/cm^3