ACT-Style: 3D Figure Applications

ACT Math · Axiom Academy

EXAMPLE ACT-Style 3D Figure Applications Finding the total volume of a composite solid — a cylinder capped by a hemisphere. A grain silo consists of a cylinder with radius 5 meters and height 12 meters, topped by a hemisphere (half-sphere) of the same radius. What is the total volume of the silo? (Use for the final estimate.) Break the silo into two standard solids: a cylinder plus a hemisphere on top. Nice work — you found the volume of a composite solid by splitting it into standard pieces and adding. Decompose: Break a composite shape into standard solids (cylinders, cones, spheres, prisms), find each volume, then add. Know the sphere formula: A sphere is , so a hemisphere is half of that, . Common denominators: To add and , write first. The ACT never gives a shape you can't decompose — spot the standard pieces, and any "weird" 3D figure becomes routine.

This is the written version of the interactive lesson above. See the full ACT Math course.