Question

1. chippewa plans to make two wildflower gardens. one bag of wildflower seed covers 200 square feet.

a. garden a is a circular garden with a diameter of 26 feet. how many square feet is garden a?
b. what is the fewest number of wildflower seed bags needed to cover garden a?
c. garden b is circular with a diameter of 52 feet. a herd member said that twice the amount of seed is needed to cover garden b. are they correct?
yes no
explain your thinking.

Explanation:

Part (a)

Step1: Find the radius of Garden A

The diameter of Garden A is 26 feet. The radius \( r \) is half of the diameter, so \( r=\frac{26}{2} = 13 \) feet.

Step2: Calculate the area of the circle

The formula for the area of a circle is \( A=\pi r^{2} \). Substituting \( r = 13 \) into the formula, we get \( A=\pi\times13^{2}=\pi\times169\approx3.1416\times169 = 530.66 \) square feet.

Step1: Determine the number of bags needed

One bag covers 200 square feet. To find the number of bags needed, we divide the area of Garden A by the area covered by one bag. So we calculate \( \frac{530.66}{200}=2.6533 \).

Step2: Round up to the nearest whole number

Since we can't buy a fraction of a bag, we need to round up to the next whole number. So we need 3 bags.

Step1: Find the radius of Garden B

The diameter of Garden B is 52 feet, so the radius \( r_{B}=\frac{52}{2}=26 \) feet.

Step2: Calculate the area of Garden B

Using the area formula \( A = \pi r^{2} \), for Garden B, \( A_{B}=\pi\times26^{2}=\pi\times676\approx3.1416\times676 = 2123.72 \) square feet.

Step3: Compare the areas

The area of Garden A is approximately 530.66 square feet. The ratio of the area of Garden B to Garden A is \( \frac{2123.72}{530.66}\approx4 \). So the area of Garden B is about 4 times the area of Garden A, not 2 times. So the HERD member is not correct.

Answer:

The area of Garden A is approximately \( 530.66 \) square feet.

Part (b)