Question

Can i have some help Please! (Brainliest As Well if it lets me) Pick question 16 or 17 to answer i only have to do one Be specific in your comparisons - think about K (dilation scale factor) and how K changed for circumference versus area. You will need to look up the formula for surface area of a sphere.

Answer 1

For problem 17, if you double the diameter of the moon, then the surface increases by a factor of 4 and the volume by a factor of 8.

How to compare the change in surface and volume?

Let's answer question 17.

Remember that for a sphere of radius R, the volume is:

$V = (4/3)*pi*R^3$

And the surface area is:

$S = 4*pi*R^2$

So the volume depends on the cube of the radius and the surface on the square of the radius.

Now, if we double the diameter of the moon, then we also double the radius.

So the new volume will be:

$V' = (4/3)*pi*(2*R)^3 = 8*[(4/3)*pi*R^3] = 8*V$

The new volume is 8 times the original volume.

And for the surface:

$S' = 4*pi*(2*R)^2 = 4*[4*pi*R^2] = 4*S$

So the new surface is 4 times the original surface.

If you want to learn more about spheres:

brainly.com/question/10171109

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