Mrs. Smith wants to build a semicircular garden, and she wants to surround it with a fence to keep out her dogs. She's measured half the garden's length at 6 m long. How much fencing material will she need to buy?
so what is the answer
I interpret that to mean the radius of the semi-circle is 6 m,
fence length = 6 + (1/2)(2π)(6)
= (6 + 6π) m
To calculate the total length of fencing material Mrs. Smith needs to buy, we need to find the circumference of the semicircular garden.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Since Mrs. Smith has measured half the garden's length at 6 m, we can use this measurement as the radius of the semicircle.
Plugging the value of the radius into the formula, we get:
C = 2π(6)
C = 12π
The total length of fencing material Mrs. Smith needs to buy is 12π meters.
To calculate how much fencing material Mrs. Smith needs to buy, we first need to find the circumference of the semicircular garden. The formula to find the circumference of a circle is C = πd, where C is the circumference and d is the diameter.
Since Mrs. Smith has measured half the garden's length (6 m), we can double it to get the diameter of the semicircle. Thus, the diameter is 2 * 6 m = 12 m.
Next, we can use the formula C = πd to find the circumference, where π is approximately 3.14.
C = 3.14 * 12m = 37.68 m
Therefore, Mrs. Smith will need to buy approximately 37.68 meters of fencing material to surround her semicircular garden.