Question

Please help!!

Answer 1

As said in the hint, what's the ratio of the lateral area of the large pyramid to that of the the smaller one?
Then think of a line, a square and a cube. Area of square = l^2, volume of cube = l^3. What does this say about doubling/tripling/scaling the radii/length of sides and its effect on areas and volumes?

Answer 2

"scale factor" means they want you to find the number by which all measures of the first pyramid have been multiplied.
if you look at a pyramid of length (on the ground) L, height H, if the scale factor is \(\alpha\), the measures in the second pyramid are \(\alpha L\) and \(\alpha H\).

When you compute an area, you multiply two quantities. The analogue computation for the side area (\(x\times y\)) is, for the bigger pyramid (\(\alpha x \times\alpha y=\alpha^2 xy\)). This should help.

Answer 3

(edit: area: \(x y/2\). but this doesn't change the fundamental fact that the two areas given in the statement allow you to find \(\alpha^2\)..

Answer 4

(area of a triangle of side \(x\) and height \(y\)...)