Question

the large sphere has a diameter of 12 feet. what is the volume of the shaded figure? express the answer in terms of π. 252π ft³ 261π ft³ 288π ft³ 324π ft³

Explanation:

Step1: Find large sphere radius

Radius $r_1 = \frac{12}{2} = 6$ ft

Step2: Volume of large sphere

Volume formula: $V_1 = \frac{4}{3}\pi r_1^3 = \frac{4}{3}\pi (6)^3 = \frac{4}{3}\pi \times 216 = 288\pi$ ft³

Step3: Volume of small sphere

Small radius $r_2=3$ ft, $V_2 = \frac{4}{3}\pi r_2^3 = \frac{4}{3}\pi (3)^3 = \frac{4}{3}\pi \times 27 = 36\pi$ ft³

Step4: Subtract volumes for shaded area

Shaded volume $V = V_1 - V_2 = 288\pi - 36\pi$

Answer:

252π ft³