Question

a metal sheet has circles of the same size cut from a rectangular sheet of metal as shown.
what is the approximate area of the metal sheet in square inches after the circles are cut out? use 3.14 for π. round your answer to the nearest hundredth.
use the number pad to enter your answer in the box.

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 26\) inches and \(w=12.3\) inches. So, \(A_{rectangle}=26\times12.3 = 319.8\) square inches.

Step2: Calculate the area of one circle

The formula for the area of a circle is \(A=\pi r^{2}\). The diameter of each circle is \(12.3\div3 = 4.1\) inches, so the radius \(r=\frac{4.1}{2}=2.05\) inches. Using \(\pi = 3.14\), \(A_{circle}=3.14\times(2.05)^{2}=3.14\times4.2025 = 13.19585\) square inches.

Step3: Calculate the area of three circles

Since there are three circles, \(A_{three - circles}=3\times13.19585 = 39.58755\) square inches.

Step4: Calculate the area of the metal sheet after the circles are cut out

\(A = A_{rectangle}-A_{three - circles}\). So, \(A=319.8 - 39.58755=280.21245\approx280\) square inches.

Answer:

280