A necklace is made up of 50 spherical beads. Each bead has a radius of 8 millimeters. What is the volume of the necklace? What is the surface area?
v = 50 * 4pi/3 * 8^3
a = 50 * 4pi * 8^2
To calculate the volume and surface area of the necklace, we first need to calculate the volume and surface area of one bead, and then multiply it by the total number of beads.
The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where V is the volume and r is the radius.
In this case, the radius of each bead is given as 8 millimeters, so we can substitute this value into the formula to find the volume of one bead:
V_bead = (4/3) * π * (8 mm)^3
To find the surface area of a sphere, we can use the formula A = 4 * π * r^2, where A is the surface area and r is the radius.
Substituting the given radius into the formula, we can find the surface area of one bead:
A_bead = 4 * π * (8 mm)^2
Once we have the volume and surface area of one bead, we can multiply them by the total number of beads, which in this case is 50.
Therefore, the volume of the necklace is:
Volume = V_bead * number of beads = ((4/3) * π * (8 mm)^3) * 50
And the surface area of the necklace is:
Surface area = A_bead * number of beads = (4 * π * (8 mm)^2) * 50
Calculating these values will give you the final answers.