Question

practice

1. find the area. answer to the nearest tenth.

a) b)

1. the first nations drum shown is handmade from a circular

piece of deer hide. it covers a ring with a radius of 6 inches
and evenly overhangs the top of the ring by 1 inch.
a) what is the radius of the hide used to make the drum?
b) find the area of the hide, to the nearest tenth of a
square inch.

1. in baseball, the infield is a quarter of a circle with a radius

of 95 feet. find the area of the infield, to the nearest tenth
of a square foot.

Explanation:

1a)

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle. Given \(r = 15\space cm\).

Step2: Substitute the value of \(r\) into the formula

\(A=\pi\times(15)^{2}=\pi\times225\). Using \(\pi\approx3.14159\), we get \(A = 3.14159\times225=706.85775\space cm^{2}\). Rounding to the nearest tenth, \(A\approx706.9\space cm^{2}\).

1b)

Step1: Find the radius from the diameter

Given the diameter \(d = 6\space ft\), the radius \(r=\frac{d}{2}=\frac{6}{2}=3\space ft\).

Step2: Use the area formula for a circle

Using \(A=\pi r^{2}\) with \(r = 3\space ft\), we have \(A=\pi\times(3)^{2}=9\pi\). Using \(\pi\approx3.14159\), \(A=3.14159\times9 = 28.27431\space ft^{2}\). Rounding to the nearest tenth, \(A\approx28.3\space ft^{2}\).

2a)

Step1: Calculate the radius of the hide

The radius of the ring is \(r_{ring}=6\space in\), and the overhang is \(1\space in\). So the radius of the hide \(r_{hide}=r_{ring}+ 1\). Substituting the value, \(r_{hide}=6 + 1=7\space in\).

2b)

Step1: Apply the area formula for a circle

Using \(A=\pi r^{2}\) with \(r = 7\space in\), we get \(A=\pi\times(7)^{2}=49\pi\). Using \(\pi\approx3.14159\), \(A=3.14159\times49=153.93791\space in^{2}\). Rounding to the nearest tenth, \(A\approx153.9\space in^{2}\).

3)

Step1: Recall the formula for the area of a quarter - circle

The area of a full circle is \(A=\pi r^{2}\), and the area of a quarter - circle is \(A_{quarter}=\frac{1}{4}\pi r^{2}\). Given \(r = 95\space ft\).

Step2: Substitute the value of \(r\) into the formula

\(A_{quarter}=\frac{1}{4}\times\pi\times(95)^{2}=\frac{1}{4}\times\pi\times9025\). Using \(\pi\approx3.14159\), \(A_{quarter}=\frac{3.14159\times9025}{4}=\frac{28359.84775}{4}=7089.9619375\space ft^{2}\). Rounding to the nearest tenth, \(A_{quarter}\approx7090.0\space ft^{2}\).

Answer:

1a) \(706.9\space cm^{2}\)
1b) \(28.3\space ft^{2}\)
2a) \(7\space in\)
2b) \(153.9\space in^{2}\)

1. \(7090.0\space ft^{2}\)