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Here are some tips for Area And Volume Proportions, which aligns with Florida state standards:

Area and Volume Proportions

You will need to know area and volume formulas for this topic.
To review, see the topics below:
Area Volume
Circle πr2 Sphere (4/3)πr3
Square s2 Cube s3
Rectangle lw Rectanglar Prism lwh
Triangle (1/2)bh Triangular Prism (1/2)bhl
Cylinder πr2h
s   side
l   length
w   width
h   height
b   base

Example 1: Area

Find the area of the following shapes after the transformations have been made.
A circle has an area of 11. If the radius is increased by a factor of 3, what is the new area of the circle?

Original area
original Area = 11 = π (original radius)2
New area
new Area = π (new radius)2
From the statement the radius is increased by a factor of 3, we get

 new Area = π (new radius)2 = π (3 × original radius)2 = 9 × π (original radius)2 = 9 × original Area = 9 × 11 = 99

Alternate solution:
The radius increased by 3. In the circle area equation, the radius is squared so we can square the factor 3 and multiply that by the original area to get 32 × 11 = 99.

Example 2: Volume

Find the volume of the following shapes after the transformations have been made.
A triangular prism has a volume of 20. If the base height is increased by a factor of 4, what is the new volume of the triangular prism?

Original volume
original Volume = 20 = (1/2)(base)(original height)(length)
New volume
new Volume = (1/2)(base)(new height)(length)
From the statement the base height is increased by a factor of 4, we get
new height = 4 × old height

 new Volume = (1/2)(base)(new height)(length) = (1/2)(base)(4 × old height)(length) = 4 × (1/2)(base)(old height)(length) = 4 × original Volume = 4 × 20 = 80

Alternate solution:
The base height increased by 4. In the triangular prism volume formula, the base height is linear so we can multiply the increased factor by the original volume to get 4 × 20 = 80.