The lesson explicitly gives the formulas V = πr^2h (cylinder), V = (1/3)πr^2h (cone), and V = (4/3)πr^3 (sphere) and directs students to record them on a "Volume Notes" page. Students complete multiple worked examples and problem sets for each shape where they compute volumes and work backwards to find missing measurements like height or radius (e.g., pencil cup, paint can, traffic cone, tennis ball, crystal ball). Students also apply these formulas in real-world contexts and projects (Flavor Frenzy design challenge, ice cream party) that require calculating and comparing capacities.

Students are asked to compute and manipulate volumes in multiple problems: e.g., Problem 14 asks for the height of a cylinder given volume (314 in³) and radius (5 in), Problem 15 asks for the radius of a cone given volume (150 in³) and height (10 in), and Problem 16 asks for the radius of a sphere given its volume (113.04 cm³). Several real-world contexts appear (a snow cone volume, a cylindrical water bottle) and answer keys show numeric solutions that require using V = πr²h (cylinder), V = (1/3)πr²h (cone), and V = (4/3)πr³ (sphere).

Students are instructed to measure the radius and height of a cylinder, sphere, and cone, then calculate and record each volume on a 3D Sculpture Volume Worksheet. The worksheet specifies using the value 3.14 for pi and provides a table with spaces to fill radius, height, and calculated volume for each shape, plus a total volume. An answer key gives computed volumes for a cylinder, sphere, and cone, showing numerical application of the volume calculations.

Students are asked to write the formula and compute volumes for a cylinder, cone, and sphere (Activity 4 Student Activity Page items 3–5). They calculate numerical volumes (cylinder: V = πr²h; cone: V = 1/3πr²h) and solve an inverse problem to find a sphere's radius from a given volume. The Skills list and Parent Plan explicitly state that students will "Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems."

Students are asked to compute the volume of a round pencil cup given height 4 in and radius 3 in and told to use 3.14 for pi (problem 18). Students are also asked to compute how much flavored ice will fill a snow cone cup given radius 2 in and height 6 in, again with pi = 3.14 (problem 19). The answer key provides numeric approximations (≈113.04 and ≈25.12), indicating students perform calculations applying volume formulas for a cylinder and a cone to real-world contexts.