Answer:
The surface area to volume ratio of a sphere of diameter 2.6 mm can be calculated using the formulas for the volume and surface area of a sphere. The volume of a sphere is given by the formula 4πr3/3, where r is the radius of the sphere. The surface area of a sphere is given by 4πr2. In this case, the radius is 1.3 mm (half of 2.6 mm), and the surface area to volume ratio is 4π(1.3 mm)2/4π(1.3 mm)3 = 3/2π.
Step-by-step explanation:
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.
The surface area of a sphere can be calculated using the formula A = 4πr^2, where A is the surface area and r is the radius of the sphere.
Given that the diameter of the sphere is 2.6 mm, we can calculate the radius by dividing the diameter by 2:
r = 2.6 mm / 2 = 1.3 mm
Now, we can calculate the volume of the sphere using the formula:
V = 4/3 * π * (1.3 mm)^3
We can also calculate the surface area of the sphere using the formula:
A = 4π * (1.3 mm)^2
The surface area to volume ratio (SA:V) of a sphere is the ratio between the surface area and the volume. To calculate the SA:V ratio of the sphere, we divide the surface area by the volume:
SA:V = A/V
It's important to note that the ratio will be dimensionless because surface area and volume both have units of length cubed, thus canceling each other out in the ratio.