Answer:
about 53.4 square feet more
Step-by-step explanation:
You want to know how much more space a circle with 9 ft radius has than a circle with 16 ft diameter.
Area
The formulas for area of a circle can be written as ...
A = πr²
A = (π/4)d²
We can use these two formulas to find the difference in area between the larger and smaller circles.
Difference
tree II space - tree I space
= π(9 ft)² - π/4(16 ft)² ≈ 53.4 ft²
Tree II requires about 53.4 square feet more space than tree I.
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Additional comment
We could use the same formula twice by converting the diameter to a radius, or vice versa. We can also use the factoring of the difference of squares to change the way we do the computation:
π(9 ft)² -(π/4)(16 ft)² = π(9 ft -8 ft)(9 ft +8 ft) = 17π ft² ≈ 53.4 ft²
