Question

a circular marble tabletop has a diameter of 42 inches. determine the area of the circular marble top in square inches. use 3.14 for π. round your answer to the nearest whole square inch.

Explanation:

Step1: Find the radius

The radius \(r\) of a circle is half of the diameter \(d\). Given \(d = 42\) inches, so \(r=\frac{d}{2}=\frac{42}{2}=21\) inches.

Step2: Use the area formula

The area formula of a circle is \(A=\pi r^{2}\). Substitute \(r = 21\) inches and \(\pi=3.14\) into the formula: \(A = 3.14\times21^{2}\).
First, calculate \(21^{2}=21\times21 = 441\). Then, \(A=3.14\times441\).
\(3.14\times441=(3 + 0.14)\times441=3\times441+0.14\times441=1323+61.74 = 1384.74\).

Step3: Round the result

Round \(1384.74\) to the nearest whole number. Since the decimal part \(0.74\gt0.5\), we round up. So \(1384.74\approx1385\).

Answer:

\(1385\) square inches.