A jade necklace is made up of 100 spherical jade beads. Each bead has a diameter of 7 mm. What is the total amount of jade, in cubic millimetres?
To find the total amount of jade in cubic millimeters, we need to first calculate the volume of a single jade bead and then multiply it by the 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 of the sphere.
Given that the diameter of each jade bead is 7 mm, we can calculate the radius:
radius = diameter / 2 = 7 mm / 2 = 3.5 mm
Plugging the radius into the volume formula:
V = (4/3) * π * (3.5 mm)^3
Calculating the volume:
V = (4/3) * 3.14 * (3.5 mm)^3
= (4/3) * 3.14 * 42.875 mm^3
≈ 180.96 mm^3
Now, to find the total amount of jade, we multiply the volume of a single bead by the number of beads:
total amount of jade = volume of a single bead * number of beads
= 180.96 mm^3 * 100 beads
= 18096 mm^3
Therefore, the total amount of jade in cubic millimeters is 18096 mm^3.
To find the total amount of jade in the necklace, we need to calculate the volume of each bead and then multiply it by the total number of beads.
The formula to compute the volume of a sphere is V = (4/3) * π * r^3, where V represents volume and r is the radius of the sphere.
Given that the diameter of each bead is 7 mm, the radius (r) is half the diameter, so r = 7 mm / 2 = 3.5 mm.
Now, let's substitute the values into the formula to calculate the volume of a single bead:
V = (4/3) * π * (3.5 mm)^3
To find the answer, we need to multiply the volume of a single bead by the total number of beads (100):
Total volume = (4/3) * π * (3.5 mm)^3 * 100
Let's calculate the result:
Use this formula, find the volume of 1 bead.
V=4/3πr^3
Multiply the volume of 1 bead by 100 to find the total amount of jade.