Given that d = 2r, explain how to write a formula for the diameter d of a cell given its surface area to volume quotient. (Full question below)

Question

I was out sick for a whole week and need help with concept.

//Full question//

In biology, the surface-area-to-volume quotient Q of a single spherical cell is given by the formula Q= 3/r where r is the radius of the cell. Suppose you need to calculate diameter of the cells given the surface area to volume quotients of the cells. Given that d = 2r, explain how to write a formula for the diameter d of a cell given its surface area to volume quotient.

Answer 1

Q = 3/r

 

Since d = 2r, divide both sides by 2 and you get d/2 = r.  Substitute d/2 in place of r:

 

     Q = 3/r

     Q = 3/(d/2)

 

When you divide by a fraction (d/2), it's the same as multiplying by the reciprocal of the fraction:

 

     Q = 3/(d/2) = 3*(2/d) = 6/d

     Q = 6/d

 

Multiply both sides by d:

 

     d*Q = 6

 

Finally divide both sides by Q

 

     d = 6/Q