If a spherical medicine with radius r is broken down in to the 1000 spherical small tablets then the CSA of original spherical 6 will become......times the original
600 times the original one????
@oobleck
Kindly reply
To find the ratio of the cross-sectional area (CSA) of the original spherical medicine to the combined CSA of the smaller tablets, we need to compare the surface areas of the spheres involved.
The formula for the surface area of a sphere is given by the equation:
SA = 4πr^2
Where SA is the surface area and r is the radius of the sphere.
Since the original medicine has a radius of r, its surface area (S1) can be calculated as:
S1 = 4πr^2
When the medicine is broken down into 1000 smaller tablets, each tablet will have a radius of r/10 (assuming each tablet is equal in size). The combined surface area of all the tablets (S2) can be calculated by multiplying the surface area of a single tablet by the total number of tablets:
S2 = 1000 * 4π(r/10)^2
= 4π(r/10)^2 * 1000
To find the ratio of S1 to S2, we divide S1 by S2:
Ratio = S1 / S2
= (4πr^2) / (4π(r/10)^2 * 1000)
= 10^4
Therefore, the cross-sectional area (CSA) of the original spherical medicine will become 10,000 times the original CSA when it is broken down into 1000 spherical small tablets.
try that again so it makes some sense.
CSA?
original spherical 6?
I will say that each small sphere has a radius of r/10.
Work with that.