This time I will explain about area and volume relationship.

[ area ]
when you got the area of a certain region or shape
and know the scale factor,
new area is
(old area) × (scale factor)²

for example,
The area of a triangle is 10cm².
If each side of the triangle is increased by 4,
the area of the triangle wil be...(4 is a scale factor)
10 × 4²
= 10 × 16
= 160 cm²

[ Volume ]

This time I will explain about area and volume relationship.

For volume, you should cube your scale factor to get a volume of the new shape.
New volume is
(old volume) × (scale factor)³

For example, you have two cylinders showing above,
and cylinderA's volume is 785cm³ and it is
decreased by the scale factor 2.
So, to get a cylinderB's volume..

Cylinder B * (scale factor)³ = CylinderA
Cylinder B * 2³ = 785
785/8 = Cylinder B

So the volume of CylinderB is 98.125cm³