Question

Can someone help me with this geometry question?/ the first option is 127,826,64,20

Answer 1

Step 1

Given;

`\begin{gathered} \text{Angle of sector=140}^o \\ \text{Diameter of circle=52 inches} \end{gathered}`

Required;

`\begin{gathered} To\text{ find; 1) Arc length} \\ 2)Area_{} \end{gathered}`

Step 2

Find the arc length of the land Juan has cleared by Midday

`\begin{gathered} \text{Arc length=}(\theta)/(360)*2*\pi* r \\ r=\frac{\text{ diameter}}{2}=(52)/(2)=26\text{inches} \\ \pi=(22)/(7) \\ \theta=140 \\ \end{gathered}`
`\begin{gathered} \text{Arc length=}(140)/(360)*2*(22)/(7)*26 \\ \text{Arc length= }(572)/(9)=63.555556\text{ inches} \\ \text{Arc length}\approx64inches \end{gathered}`

Hence, the land Juan has cleared by midday has an arc length of about 64 inches

Step 3

Find the area of the land

`\text{Area of a sector=}(\theta)/(360)*\pi* r^2`
`\begin{gathered} \text{Area of the land=}(140)/(360)*(22)/(7)*26^2 \\ \text{Area of the land=}(7436)/(9)=826.22222222 \\ \text{Area of the land}\approx826in^2 \end{gathered}`

Hence, the area of the land he has cleared by midday is about 826in²