Question

What is the area of this pool rounded to the tens place?

Answer 1

First, let's calculate the area of each circular sector, using the formula below:

$A=\frac{r^2\theta}{2}$

Where r is the radius and theta is the central angle.

So, using theta = 2.21 and r = 30, we have:

$A_1=\frac{30^2\cdot2.21}{2}=994.5\text{ ft^^b2}$

Both circular sectors have the same area, so A2 = A1.

The area of a triangle is given by:

$A=\frac{b\cdot h}{2}$

Where b is the base and h is the height relative to this base.

Using b = 20 and h = 25, we have:

$A_3=\frac{20\cdot25}{2}=250\text{ ft^^b2}$

The area of the triangles is the same, so A4 = A3.

Now, adding all areas, we have:

$\begin{gathered} A_{total}=A_1+A_2+A_3+A_4\\ \\ A_{total}=994.5+994.5+250+250\\ \\ A_{total}=2489\text{ ft^^b2} \end{gathered}$

Rounding to the tens, we have an area of 2490 ft², so the correct option is D.