Volume of Cylinders, Cones, & Spheres

Cluster: Solve Real-World and Mathematical Problems Involving Volume of Cylinders, Cones, And Spheres.

Task Overview: Students will use the volume formulas of cubes, rectangular prisms, and pyramids to write the formula for cones and cylinders. Students have been taught that the volume of a former three-dimensional shapes is Volume = B (area of the base) * h (height). Students will then draw correlations to the volume formula of a sphere. Students will use their understanding of the formulas to solve for missing lengths.

8.G.A.1 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

This standard focuses on the volume formulas for 3-dimensional shapes related to circles (cones, cylinders and spheres). Students have already worked with volume of cubes and rectangular prisms. They apply these same understandings beginning with cylinders.

Objectives

Students should be able to find the volume of cylinders, cones, and spheres.
Students should be able to find the missing lengths of the radius and height given the volume of certain 3D shapes.

Additional/Prerequisite Skills:

• Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. (8.EE.A.2)
• Students will need to use substitution for the given measurements.
• Rounding to the nearest tenth or hundredth place.