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Use the image at the right to answer the question below.
5. Two different trees are being planted in an outdoor garden. Each tree requires a specific
amount of space for the roots to grow. How much more space will tree II require?

Use the image at the right to answer the question below 5 Two different trees are being planted in an outdoor garden Each tree requires a specific amount of sp class=

Respuesta :

sqdancefan

Answer:

Ā  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 ...

Ā  A = Ļ€rĀ²

Ā  A = (Ļ€/4)dĀ²

We can use these two formulas to find the difference in area between the larger and smaller circles.

Difference

Ā  Ā tree II space - tree I space

Ā  = Ļ€(9 ft)Ā² - Ļ€/4(16 ft)Ā² ā‰ˆ 53.4 ftĀ²

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:

Ā  Ļ€(9 ft)Ā² -(Ļ€/4)(16 ft)Ā² = Ļ€(9 ft -8 ft)(9 ft +8 ft) = 17Ļ€ ftĀ² ā‰ˆ 53.4 ftĀ²

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