Question

The surface area-to-volume ratio of cells determines how quickly they can absorb materials. Suppose that a space mission to Planet Zognard-42 uncovers giant cube-shaped single celled organisms living in an oxygen atmosphere. One species of cube-shaped organism is 2 cm on each side. Another is 1 cm on each side. About how much faster will the smaller cube organism be able to absorb oxygen? A) 2 times B) 3 times C) 6 times D) They will absorb at the same rate.

Answer 1

species one has a sa of 24 (2*2*6) and a volume of 8 (2*2*2) so I'll make that a ratio of 1:3

species two has a sa of 6 (1*1*6) and a volume of 1 (1*1*1) so I'll make that a ratio of 1:6

2*3=6 so it will absorb oxygen twice as fast

Answer 2

Option , A Smaller species will absorb oxygen 2 times faster than the larger species.

Step-by-step explanation:

The amount of material absorbed by cells is directly determined by the surface area-to-volume ratio of cells.

A) Species 1 is of cube shape with sides of 2 cm

B) Species 2 is of cube shape with sides of 1 cm

Now we will evaluate the surface area-to-volume ratio for both the species

1) Species 1 -

Volume of a cube is
`a^(3)`

Surface area of a cube is
`6a^(2)`

surface area-to-volume ratio
`= (6a^(2) )/(a^(3) ) \\= (6)/(a)`

Here

`a = 2 \\`

surface area-to-volume ratio for species 1 is
`(6)/(2) \\= 3`

1) Species 2 -

Volume of a cube is
`a^(3)`

Surface area of a cube is
`6a^(2)`

surface area-to-volume ratio
`= (6a^(2) )/(a^(3) ) \\= (6)/(a)`

Here

`a = 1 \\`

surface area-to-volume ratio for species 1 is
`(6)/(1) \\= 6`

Species 2 (the smaller one) will absorb oxygen 2 times faster than the larger species.

Hence, Option A is correct