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.

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

The volume of the figure is exactly \(\boxed{\phantom{0}}\) (Type an exact answer in terms of π. Si

square inches. inches. cubic inches.

Solution

Find the volume of the sphere using the formula for the volume of a sphere: The formula for the volume \( V \) of a sphere is: \[ V = \frac{4}{3} \pi r^3 \] The radius \( r \) of the sphere is 9 inches. Substitute \( r = 9 \) into the formula: \[ V = \frac{4}{3} \pi (9)^3 \] Calculate \( 9^3 \): \[ 9^3 = 729 \] Now substitute back: \[ V = \frac{4}{3} \pi (729) \] Calculate \( \frac{4}{3} \times 729 \): \[ \frac{4}{3} \times 729 = 972 \] So, the volume is: \[ V = 972\pi \] The volume of the sphere is exactly \( 972\pi \) cubic inches. Now, round to the nearest whole number. Use \( \pi \approx 3.14159 \): \[ 972 \times 3.14159 \approx 3057.26 \] Rounded to the nearest whole number, the volume is approximately 3057 cubic inches.