Answer: 42.75π
Step-by-step explanation:
The volume of a frustum can be determined by the formula [tex]V= \frac{\pi H}{3}(R^2 + Rr + r^2)[/tex]; however, it is much easier to calculate it by subtracting the volume of the smaller cone from the volume of the bigger cone. The volume of a single cone has a much more manageable formula, [tex]V = \frac{1}{3} \pi r^2 h[/tex], where r is the radius of the base of the cone and h is the height of the cone from the tip to the base.
The small cone's base and height are 3 cm and 6 cm respectively, while the large cone's base and height are 4.5 cm and (6+3) = 9cm respectively.
Volume of Small Cone: [tex]V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (3)^2 (6) = 18\pi[/tex]
Volume of Large Cone: [tex]V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (4.5)^2 (9) = 60.75\pi[/tex]
Volume of Frustum = [tex]60.75\pi -18\pi = 42.75\pi[/tex]
Hope this helps. Please reply below if you have any further questions.
