Question: Find the volume of the figure. Express the answer in terms of π and then round to the nearest whole…

Find the volume of the figure. Express the answer in terms of π and then round to the nearest whole number.

[Diagram of a sphere with a diameter of 9 inches]

The volume of the figure is exactly \(972\pi\) cubic inches. (Type an exact answer in terms of π. Simplify your answer.)

The volume of the figure is approximately [ ] (Round to the nearest whole number as needed.)

[Dropdown options: inches, square inches, cubic inches]

Solution

To find the approximate volume of a sphere with a radius of 9 inches, we can use the formula for the volume of a sphere: \[ V = \frac{4}{3} \pi r^3 \] Substitute the radius \( r = 9 \) inches into the formula: \[ V = \frac{4}{3} \pi (9)^3 \] Calculate \( 9^3 \): \[ 9^3 = 729 \] Substitute \( 729 \) back into the formula: \[ V = \frac{4}{3} \pi \times 729 \] Calculate \(\frac{4}{3} \times 729\): \[ \frac{4}{3} \times 729 = 972 \] So, the exact volume in terms of \(\pi\) is: \[ 972\pi \text{ cubic inches} \] To find the approximate volume, multiply by \(\pi \approx 3.14159\): \[ V \approx 972 \times 3.14159 \] \[ V \approx 3056.57 \] Rounding to the nearest whole number, the volume of the sphere is approximately: \[ 3057 \text{ cubic inches} \]