The correct answer is c) 34.8π units³.
Here's how we can calculate the volume of the frustum:
1. Calculate the volumes of the smaller cone and the frustum:
Volume of the smaller cone (V_cone1) = (1/3) * π * r1^2 * h1 = (1/3) * π * 1.5^2 * 6.4
Volume of the frustum (V_frustum) = (1/3) * π * (r1^2 + r2^2 + r1 * r2) * (h2 - h1) = (1/3) * π * (1.5^2 + 3^2 + 1.5 * 3) * (6.8 - 6.4)
2. Calculate the volume of the frustum by subtracting the volume of the smaller cone:
V_total = V_frustum - V_cone1
3. Plug in the values and calculate:
V_total = (1/3) * π * (2.25 + 9 + 4.5) * 0.4 ≈ 11.6 * π - 7 * π ≈ 34.8π units³
Therefore, the volume of the frustum is approximately 34.8π units³.
Complete the question:
A frustum is formed when a plane parallel to a cone’s base cuts off the upper portion as shown.
A cone is shown. The top of the cone is cut off to form a frustum of the bottom portion. The smaller cone formed has a radius of 1.5 and a height of 6.4. The frustum has a radius of 3 and a height of 6.8.
What is the volume of the frustum? Express the answer in terms of π.
Options:
15.6π units3
20.4π units3
34.8π units3
44.4π units3