Transcript Surface Area to volume - Science-with

• What does the city do with
wastes?
• How does a city get new
nutrients?
• Just like a city, a cell needs to receive
nutrients and remove wastes.
• This is done through the cell
membrane.
• At what point, does it become too hard
to transport materials in and out? In
other words...
How Big is Too Big?
• All living organisms are made up of cells.
• Cells are really small. Why?
• Why can’t a human be made of just one
big cell instead?
• All cells diffuse nutrients and wastes in
and out at a constant rate.
• Basically, the more surface area (aka cell
membrane), the more nutrients and
wastes a cell can exchange.
• Using the formulas for volume and surface
area, we can make a ratio to compare the
two.
Surface Area to Volume
Assignment
• Follow along for two examples then
complete the rest of the assignment using
the formulas provided.
• Ratio: SA / V
Surface Area to Volume Ratio
• If we were to watch nutrients being absorbed at a constant rate in 3 different
size cubes, the nutrients could reach the entire cytoplasm of smaller cells
because, for their volume, they had a much larger surface area.
2 cm3
4cm3
1 cm3
Dead: nutrients can’t get to
all parts of the cell.
Surface Area =
but still
Alive! Nutrients make it to
TheBetter,
smaller
the cell,
dead.
all parts of the cell.
the larger the SA / V ratio, and the
(base) (height)
easieradded
it isup
for
to reach
fordiffusion
all sides
all parts of the cell
S.A.= (4cm)(4cm)(6 sides)
S.A.= (2cm)(2cm)(6 sides)
S.A.= (1 cm)(1cm)(6sides)
= 96 cm2 x 1 cube = 96 cm2
= 24 cm2 x 8 cubes = 192 cm2
= 6 cm2 x 64 cubes = 384 cm2
Volume = (base) (width) (height)
V = (4cm)(4cm)(4cm)
= 64cm3 x 1 cube = 64cm3
Surface Area
Volume
S.A. 96

1.5
V
64
V = (2cm)(2cm)(2cm)
= 8cm3 x 8 cubes = 64 cm3
S . A. 192

3
V
64
V = (1cm)(1cm)(1cm)
= 1cm3 x 64 cubes = 64 cm3
S . A. 384

6
V
64
• Shape also affects surface area to volume ratio.
16
7.11
• Skinnier, flatter
cells large SA / V
ratios.
• Cells with
projections, like
microvilli, have
large SA / V ratios.
• In order for an organism to be large, it must be
multi cellular.
• Which of the equal volumes below has the
greatest SA / V Ratio and is therefore most likely
to survive?
• Distribution systems, such
as your circulatory system
deliver nutrients to and
remove waste from each cell.
• Diffusion is sufficient
because of each cell’s large
SA / V ratio.