We are asked to find the volume of the given frustum.
Recall that the volume of a frustum is given by
[tex]V=\frac{1}{3}\cdot h\cdot(B_1+B_2+\sqrt[]{B_1B_2})[/tex]
Where h is the height, B₁ is the lower area and B₂ is the upper base area of the frustum.
The lower base area (B₁) is given by
[tex]B_1=\pi r^2_1=\pi(21)^2=441\pi\: in^2[/tex]
The upper base area (B₂) is given by
[tex]B_2=\pi r^2_2=\pi(7)^2=49\pi\: in^2[/tex]
Finally, substitute all the values into the above volume formula
[tex]\begin{gathered} V=\frac{1}{3}\cdot h\cdot(B_1+B_2+\sqrt[]{B_1B_2}) \\ V=\frac{1}{3}\cdot24\cdot(441\pi+49\pi_{}+\sqrt[]{441\pi\cdot49\pi}) \\ V=\frac{1}{3}\cdot24\cdot(441\pi+49\pi_{}+147\pi) \\ V=\frac{1}{3}\cdot24\cdot(637\pi) \\ V=\frac{1}{3}\cdot15288\pi \\ V=5096\pi\: in^3 \end{gathered}[/tex]
Therefore, the volume of the frustum is 5096π cubic inches.
