Question
If a spherical medicine with radius R is broken down into 1000 spherical small tablets then the surface area of original medicine will become ----------times. Please show method how to do
Answers
Reiny
volume of original sphere
= (4/3)π R^3
volume of each of the 1000 smaller ones
= (4/3000)π R^3
= (1/750) π R^3
let the radius of the smaller be r
4/3 π r^3 = (1/750) π R^3
r^3 = (1/1000) R^3
r = R/10
surface area of smaller = 4π r^2
= 4π R^2/100
= π R^2/25
= (4/3)π R^3
volume of each of the 1000 smaller ones
= (4/3000)π R^3
= (1/750) π R^3
let the radius of the smaller be r
4/3 π r^3 = (1/750) π R^3
r^3 = (1/1000) R^3
r = R/10
surface area of smaller = 4π r^2
= 4π R^2/100
= π R^2/25