Surface area?

Look at the using maths box below. Show that the pattern in the surface area to volume ratio continues for a cube side:
a) 0.1 cm
b) 10m

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1 Answer
Surya K.
Feb 12, 2018

See below.

Explanation:

Let's do a) first.
We can predict, by the box, that the ratio will be #60#/#"cm"#

The formula for the surface area of a cube is #6s^2#, where #s# is the side length. The volume of a cube is #s^3#.

For #0.1cm,# the surface area is

#6*0.1^2#

#6*0.01#

#0.06cm^2#

The volume is

#0.1^3#

#0.001cm^3#

The ratio is #0.06:0.001,# which is equal to #60#/#"cm"#.

Now for b).
We can predict the ratio will be #0.006#/#"cm"#

For #10m#, or #1000cm,# the surface area is:

#6*1000^2#

#6*1000000#

#6000000cm^2#

The area is

#1000^3#

#1000000000cm^3#

The ratio is #6000000:1000000000#, which is equal to #0.006#/#"cm"#.

The two have been proved.

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