5. Find the volume of a sphere with a radius of 7 ft . Use 3.14 for \( \pi \). You may round to the nearest hundredth when necessary. a \( 2547.12 \mathrm{ft}^{3} \) b \( 4578.12 \mathrm{ft}^{3} \) c \( 1436.03 \mathrm{ft}^{3} \) d \( 3257.36 \mathrm{ft}^{3} \)

To find the volume of a sphere, you can use the formula \( V = \frac{4}{3} \pi r^3 \). Plugging in the radius of 7 ft and using \( \pi \) as 3.14, the calculation goes as follows: \[ V = \frac{4}{3} \times 3.14 \times (7)^3 \] This simplifies to: \[ V = \frac{4}{3} \times 3.14 \times 343 \approx \frac{4}{3} \times 1077.72 \approx 1436.03 \] So, the correct answer is c \( 1436.03 \mathrm{ft}^{3} \). Did you know spheres are not just found in math? They appear everywhere in nature, from the simple bubbles formed in soap to the planets in our solar system! Their symmetrical shape makes them incredibly efficient for enclosing volume, which is why most fruits are round—think of how much juicy goodness fits in an orange! When working with formulas for volume, common mistakes often occur with the order of operations. Always remember to calculate the cube of the radius before multiplying with π and the fraction. A simple slip can lead to drastically different results, so double-checking your work can save you from going down the wrong mathematical path!