When a spherical cell increase in diameter from 2um to 20um, by what factor does its surface area change?

Question

By what factor does its volume change? I got this question in Biology class and I don't understand it, can someone help me? My teacher gave me this extra information: The surface area of a sphere =4(3.14) radius to the 2nd power, and the volume of a sphere =4/3(3.14) radius to the 3rd power. Diameter = 2 x radius.

Answer 1

100 and 1000, respectively. Surface area is proportional to the square of the radius, so if a cell's surface ares is 4πr², then the surface are of a cell with 10 times the radius is 4π(10r)² = 100(4πr²). Similar logic applies to volume (which is proportional to the cube of the radius).

Answer 2

If the diameter is 2um (micrometers) then the radius is half that, 1um
the surface area of the sphere is then 4*3.14*1^(2) = 12.57um^2

in the swollen cell the diameter is 20um and the radius is 10um
the surface area of the swollen cell is then 4*3.14*10^(2) = 1256.64um^2

Which means that even though the cell gout twice as big across, its surface area was increased by 100X.

You can use the same approach to show that the volume increases by 1000X!

Answer 3

Spherical Cell

Answer 4

Ok, so the surface area of the 2 um sphere would be
16pi

The surface area of the 20 um sphere would be
1600pi

So the factor the surface area changes by is 100.

Answer 5

You are looking for the factor the surface area increase?

Since the radius increase by a factor of 10, then

Surface area = 4 (pi) (r^2)
Surface area = 4 (3.14) ((10r)^2)
Surface area = 4 (pi)(100)(r^2)
Surface area = 400 (pi) (r^2)

Therefore the surface area increase by a factor of 100. Actually you can compute for the original surface area and the new surface area and compare them. But it will be much time consuming.

But I will show you.

original surface area = 4*3.14*(2um)squared = 50.24 um
new surface area = 4*3.14*(20um)squared = 5024 um

As you can see, the new surface area is 100 times the original surface area.
Therefore there was a factor of 100 increase in the surface area

Answer 6

that is particularly no longer all that complicated in case you recognize that quantity is a cube and floor section. one million) the unique volume replaced into (4?/3) * 6^3. The six grew to grow to be a 9 and boost of fifty% = 0.5, however the only million is maintained, so the ratio of volumes is ((one million.5)^3) = 3.375 So it greater suitable from the unique to ((one million.5)^3) the dimensions of the unique. i'm going to do the mathematics for this one (4?/3) * 6^3 = (216 * 4?) / 3 = (seventy two * 4?) = 288? (4?/3) * 9^3 = (729 * 4?) / 3 = 972? although by utilising the easy technique that I pronounced, take the 288? and multiply it by utilising (one million.5)^3, getting: 972 ? All that artwork wasn't needed. -------------------- considering floor section is a squared thought, only take the exterior section ?, considering A = 4?r^2 so it will boost from the unique 4? * (6^2) to (4? * 6^2) * (one million.5)^2 = (4? * 6^2) * 2.25. -------------------- only remember that quantity is cubed and section is squared and you do no longer could waste a great sort of time. that is genuinely geometry. .

Answer 7

grilled cheese