Question

a un cartón rectangular que mide 21 in de largo y 14 in de ancho se le cortó un semicírculo, como se ve a continuación. hallar el área del cartón que queda. utilizar el valor 3.14 para π, sin redondear la respuesta. incluir las unidades correctas en la respuesta.

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=length\times width\). Here, \(length = 21\) in and \(width=14\) in. So, \(A_{rectangle}=21\times14 = 294\) \(in^{2}\).

Step2: Calculate the area of the semicircle

The diameter of the semicircle \(d = 14\) in, so the radius \(r=\frac{d}{2}=\frac{14}{2}=7\) in. The formula for the area of a circle is \(A_{circle}=\pi r^{2}\), and for a semicircle \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Substituting \(\pi = 3.14\) and \(r = 7\) in, we get \(A_{semicircle}=\frac{1}{2}\times3.14\times7^{2}=\frac{1}{2}\times3.14\times49 = 76.93\) \(in^{2}\).

Step3: Calculate the remaining area of the carton

The remaining area \(A = A_{rectangle}-A_{semicircle}\). So, \(A=294 - 76.93=217.07\) \(in^{2}\).

Answer:

\(217.07\) \(in^{2}\)