Question

geometry review

1. a park is circular shaped with a radius of 2 miles. if you walk halfway around the park, how far will you walk?
2. bill wants to carpet a rectangular room that is 12 ft. by 10 ft. if carpet costs $12 per square foot, what will be the cost of the carpet?
3. the radius of a circular racetrack is 7 miles. if you drive three laps around the track, how many miles will be traveled?
4. a developer has a lot that is 1,200 feet by 800 feet. if he wants to divide it into 24 equally sized sections, how many square feet will be in each section?
5. sara wants to trim a square window with sides 24 inches. how many inches of trim does she need?
6. jill wants to sew a circular emblem that has a diameter of 6 inches. how many square inches of cloth will she need?

Explanation:

1.

Step1: Calcular la circunferencia total

La fórmula de la circunferencia de un círculo es \(C = 2\pi r\). Dado que \(r = 2\) millas, entonces \(C=2\pi(2)=4\pi\) millas.

Step2: Calcular la distancia de la mitad de la circunferencia

Como se camina la mitad de la circunferencia, la distancia \(d=\frac{4\pi}{2}=2\pi\approx 2\times 3.14 = 6.28\) millas.

Step1: Calcular el área del salón

El área de un rectángulo es \(A = l\times w\). Aquí, \(l = 12\) ft y \(w = 10\) ft, entonces \(A=12\times10 = 120\) pies cuadrados.

Step2: Calcular el costo total

Si el costado por pie cuadrado es de \(\$12\), entonces el costo total \(C=120\times12=\$1440\).

Step1: Calcular la circunferencia del circuito

La fórmula de la circunferencia de un círculo es \(C = 2\pi r\). Dado que \(r = 7\) millas, entonces \(C = 2\pi(7)=14\pi\) millas.

Step2: Calcular la distancia de tres vueltas

Si se dan tres vueltas, la distancia \(d = 3\times14\pi=42\pi\approx42\times3.14 = 131.88\) millas.

Answer:

\(6.28\) millas

2.