What is the Surface area of a glass bead that has the diameter of 11m? Express your answer to the nearest square mm.
A glass bead would be a sphere. So the formula for that is-->
SA = 4ðr^2
= 4ð(5.5^2)
= 380mm^2
is the diameter 11mm? Then
radius= .0055m
radius^2= 5.5E-3 ^ 2=30.25 E-6m
4PIr^2= about 12*30.25E-6 m
To find the surface area of a glass bead with a diameter of 11m, you can use the formula for the surface area of a sphere, which is SA = 4πr^2. Here's how to calculate it step by step:
1. Start by finding the radius of the sphere. The diameter is given as 11m, so to find the radius, divide the diameter by 2:
Radius (r) = Diameter / 2
= 11m / 2
= 5.5m
2. Now, substitute the radius into the formula for surface area:
SA = 4πr^2
= 4π(5.5m)^2
3. To express the answer in square millimeters, you need to convert meters to millimeters. Since 1 meter is equal to 1000 millimeters, you can multiply the surface area by (1000mm/m)^2:
SA = 4π(5.5m)^2 * (1000mm/m)^2
4. Calculate the surface area using the value of π (pi) as approximately 3.14159:
SA ≈ 4 * 3.14159 * (5.5m)^2 * (1000mm/m)^2
5. Simplify and calculate the result:
SA ≈ 4 * 3.14159 * 30.25m^2 * (1,000,000mm^2/m^2)
≈ 4 * 3.14159 * 30.25 * 1,000,000 mm^2
≈ 380,130,732.79 mm^2
So, the surface area of the glass bead is approximately 380,130,732.79 mm^2 to the nearest square millimeter.
To calculate the surface area of a sphere, you can use the formula SA = 4πr^2, where r is the radius of the sphere. In this case, you are given the diameter of the glass bead, which is 11m. To find the radius, you divide the diameter by 2:
radius = diameter / 2 = 11m / 2 = 5.5m
Now that you have the radius, you can substitute it into the formula:
SA = 4π(5.5^2)
Calculating this expression gives:
SA ≈ 4π(30.25)
Now, you can approximate the value of π as 3.14 and perform the multiplication:
SA ≈ 4 * 3.14 * 30.25
SA ≈ 380 mm^2
Therefore, the approximate surface area of the glass bead is 380 square millimeters.