5. How many cubic feet of soil would be required to cover a circular garden with a diameter of 8 feet if the soil needs to be 0.5 feet deep (use \( \pi=3.14 \) )? (A) \( 6.28 \mathrm{ft}^{3} \) (B) \( 12.56 \mathrm{ft}^{3} \) (C) \( 25.12 \mathrm{ft}^{3} \) (D) \( 100.48 \mathrm{ft}^{3} \) (E) \( 200.96 \mathrm{ft}^{3} \)

To find the volume of soil required to cover the garden, we first calculate the area of the circular garden using the formula \( A = \pi r^2 \). The radius \( r \) is half of the diameter, so \( r = 4 \) feet. Plugging the values in, we get: \[ A = 3.14 \times (4^2) = 3.14 \times 16 = 50.24 \, \text{ft}^2. \] Now, to find the volume, we multiply the area by the depth of the soil: \[ V = A \times \text{depth} = 50.24 \, \text{ft}^2 \times 0.5 \, \text{ft} = 25.12 \, \text{ft}^3. \] Therefore, the answer is (C) \( 25.12 \mathrm{ft}^{3} \). Calculating area and volume can sometimes be mind-bending, so it's handy to remember your formulas! Whenever you're working with circular dimensions, the key is to always convert the diameter to a radius first, as many calculations rely on that radius. It’s like getting the best seat at the movies – you can’t sit through the film without knowing where to sit! For those curious about spheres, gardens, or any other circular wonders, ponder this: if you expand that garden into a three-dimensional dome and wanted to fill it with soil, you’d need to explore volumes of spheres and hemispheres! There’s a whole world of geometric shapes out there just waiting to be explored.