Surface area?

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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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Answer 1 · 2018-02-12T11:53:43

See below.

Explanation:

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

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

For $0.1 c m,$ $0.1cm,$ the surface area is

$6 \cdot {0.1}^{2}$ $6*0.1^2$

$6 \cdot 0.01$ $6*0.01$

$0.06 c m^{2}$ $0.06cm^2$

The volume is

${0.1}^{3}$ $0.1^3$

$0.001 c m^{3}$ $0.001cm^3$

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

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

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

$6 \cdot 1000^{2}$ $6*1000^2$

$6 \cdot 1000000$ $6*1000000$

$6000000 c m^{2}$ $6000000cm^2$

The area is

$1000^{3}$ $1000^3$

$1000000000 c m^{3}$ $1000000000cm^3$

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

The two have been proved.

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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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

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