Question

visual reading tool: surface area to volume ratio in cells

1. for a cell to function efficiently, the surface - area - to - volume ratio needs to be large. in

the table below, determine the surface area to volume ratio and write the ratio in the box
provided. dont forget units, and make sure the final ratio is in relation to 1.
ratio of surface area to volume in cells
surface area
(length × width)
× 6 sides
__××=__
__××=__
__××=__
volume
(length × width
× height)
__××=__
__××=__
__××=__
ratio of surface
area to volume
__/=:__
__/=:__
__/=:__

Explanation:

Step1: Calculate the surface area of the first cube

The formula for the surface area of a cube is \(6\times(\text{length}\times\text{width})\). For a cube with length \(1\) cm and width \(1\) cm, the surface area is \(6\times(1\times1)=6\) \(cm^{2}\).

Step2: Calculate the volume of the first cube

The formula for the volume of a cube is \(\text{length}\times\text{width}\times\text{height}\). For a cube with length \(1\) cm, width \(1\) cm and height \(1\) cm, the volume is \(1\times1\times1 = 1\) \(cm^{3}\).

Step3: Calculate the surface - area - to - volume ratio of the first cube

The ratio is \(\frac{6}{1}=6:1\).

Step4: Calculate the surface area of the second cube

For a cube with length \(2\) cm and width \(2\) cm, the surface area is \(6\times(2\times2)=24\) \(cm^{2}\).

Step5: Calculate the volume of the second cube

For a cube with length \(2\) cm, width \(2\) cm and height \(2\) cm, the volume is \(2\times2\times2=8\) \(cm^{3}\).

Step6: Calculate the surface - area - to - volume ratio of the second cube

The ratio is \(\frac{24}{8}=3:1\).

Step7: Calculate the surface area of the third cube

For a cube with length \(3\) cm and width \(3\) cm, the surface area is \(6\times(3\times3)=54\) \(cm^{2}\).

Step8: Calculate the volume of the third cube

For a cube with length \(3\) cm, width \(3\) cm and height \(3\) cm, the volume is \(3\times3\times3 = 27\) \(cm^{3}\).

Step9: Calculate the surface - area - to - volume ratio of the third cube

The ratio is \(\frac{54}{27}=2:1\).

Answer:

Surface Area (\((\text{length}\times\text{width})\times6\) sides)	Volume (\(\text{length}\times\text{width}\times\text{height}\))	Ratio of Surface Area to Volume
\(2\times2\times6 = 24\) \(cm^{2}\)	\(2\times2\times2 = 8\) \(cm^{3}\)	\(24/8=3:1\)
\(3\times3\times6 = 54\) \(cm^{2}\)	\(3\times3\times3=27\) \(cm^{3}\)	\(54/27 = 2:1\)