Solve.
-Determine the area of a circular enclosure and a square enclosure made with 107 meters of fence.
A) Circular: $911 \mathrm {~m} ^ { 2 }$; square: $716 \mathrm {~m} ^ { 2 }$
B) Circular: $621 \mathrm {~m} ^ { 2 }$; square: $716 \mathrm {~m} ^ { 2 }$
C) Circular: $621 \mathrm {~m} ^ { 2 }$; square: $2862 \mathrm {~m} ^ { 2 }$
D) Circular: $911 \mathrm {~m} ^ { 2 }$; square: $2862 \mathrm {~m} ^ { 2 }$

Question

Solve.
-Determine the area of a circular enclosure and a square enclosure made with 107 meters of fence. 
A) Circular: $911 \mathrm {~m} ^ { 2 }$; square: $716 \mathrm {~m} ^ { 2 }$
B) Circular: $621 \mathrm {~m} ^ { 2 }$; square: $716 \mathrm {~m} ^ { 2 }$
C) Circular: $621 \mathrm {~m} ^ { 2 }$; square: $2862 \mathrm {~m} ^ { 2 }$
D) Circular: $911 \mathrm {~m} ^ { 2 }$; square: $2862 \mathrm {~m} ^ { 2 }$

Quizplus · Accepted Answer

For the circular enclosure, the perimeter (circumference) is given as $107 \mathrm{m}$. The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius. Solving for $r$ gives $r = \frac{107}{2\pi}$. The area of a circle is $A = \pi r^2$, substituting $r$ gives $A = \pi \left(\frac{107}{2\pi}\right)^2 \approx 911 \mathrm{m}^2$. For the square enclosure, the perimeter is $107 \mathrm{m}$, and since a square has four equal sides, each side is $\frac{107}{4} = 26.75 \mathrm{m}$. The area of a square is $side^2$, so $26.75^2 = 716 \mathrm{m}^2$.

Solve -Determine the Area of a Circular Enclosure and a Square

Solve
-Determine the Area of a Circular Enclosure and a Square