First find the area of the circular garden. The area of a circle is given by $A=\pi r^2$. With radius $6$, the area is $\pi (6{)}^2=36\pi$ square feet. Since the mulch costs $2$ dollars per square foot, multiply the area by $2$: $2\cdot 36\pi =72\pi$. So the total cost is $72\pi$ dollars.

Let the width be $w$ inches. Then the length is $3w$ inches. The area is width times length, so $w(3w)=48$. This gives $3w^2=48$, so $w^2=16$ and $w=4$ because a width must be positive. Then the length is $3(4)=12$. The perimeter is $2(12+4)=2(16)=32$. So the correct answer is $32$.

The area of a full circle with radius $r$ is $\pi r^2$. A semicircle is half of a circle, so divide that area by 2:

Therefore, the equivalent expression is $\frac{1}{2}\pi r^2$.

The horizontal side length is the difference between the $x$-coordinates: $7-1=6$. The vertical side length is the difference between the $y$-coordinates: $5-2=3$. The area of a rectangle is length times width, so the area is $6\times 3=18$ square units. Therefore, the correct answer is $18$.

Let the width be $w$ feet. Then the length is $w+3$ feet. The perimeter of a rectangle is $2l+2w$, so

Simplify:

Then the length is $6+3=9$. The area is

So the correct answer is $54$.