Question

e figure below shows a circular park. its diameter is 26 yd.
(a) use the calculator to find the area and circumference of the park. use 3.14 for π in your calculations, and do not round your answers. make sure to include the correct units.
area:
circumference:
(b) the park will be covered by artificial turf. which measure would be used in finding the amount of turf needed?
○ circumference ○ area
(c) a rope will be placed around the park. which measure would be used in finding the amount of rope needed?
○ circumference ○ area

Explanation:

Step1: Encontrar el radio

El diámetro es 26 yd, así que el radio \( r = \frac{26}{2} = 13 \) yd.

Step2: Calcular el área

La fórmula del área de un círculo es \( A = \pi r^2 \). Sustituyendo \( \pi = 3.14 \) y \( r = 13 \):
\( A = 3.14 \times 13^2 = 3.14 \times 169 = 530.66 \) \( \text{yd}^2 \).

Step3: Calcular la circunferencia

La fórmula de la circunferencia es \( C = \pi d \) (o \( C = 2\pi r \)). Sustituyendo \( \pi = 3.14 \) y \( d = 26 \):
\( C = 3.14 \times 26 = 81.64 \) yd.

Step4: Resolver (b)

La cantidad de césped artificial se refiere al área del círculo, así que se usa el área.

Step5: Resolver (c)

La cantidad de cuerda alrededor del parque se refiere a la circunferencia del círculo, así que se usa la circunferencia.

Answer:

(a) Área: \( 530.66 \text{ yd}^2 \), Circunferencia: \( 81.64 \text{ yd} \)
(b) Área
(c) Circunferencia