Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 15
Math
Unit 7
8th Grade
Lesson 15 of 16
Jump To
Solve real-world and mathematical problems involving the volume of spheres.
The core standards covered in this lesson
8.G.C.9 — Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
The foundational standards covered in this lesson
7.G.B.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.B.6 — Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Watch this video demonstration: Cylinder, Cone, and Sphere Volume. (Note, the beginning of the video reviews the volume of a cone; the demonstration of a sphere's volume starts at 1:30.)
a. What is the relationship between the volume of a cylinder and the volume of a sphere with the same diameter and height?
b. A sphere is enclosed in a cylinder. The diameter of the sphere is equal to the height of the cylinder.
The cylinder below has a diameter of 14 inches and a height of 18 inches.
What is the volume of the largest sphere that will fit in the cylinder?
The volume of an inflated beach ball is $${288\pi \space \mathrm{cm}^3}$$. What is the radius of the ball?
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
A standard soccer ball measures $${22 \space \mathrm{cm}}$$ in diameter.
What is the volume of a standard soccer ball? Give your answer to the nearest whole cubic centimeter.
An example response to the Target Task at the level of detail expected of the students.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 14
Lesson 16
Topic A: Irrational Numbers and Square Roots
Define, evaluate, and estimate square roots.
8.EE.A.2
Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.
8.NS.A.1 8.NS.A.2
Locate irrational values approximately on a number line. Compare values of irrational numbers.
8.NS.A.2
Represent rational numbers as decimal expansions.
8.NS.A.1
Represent decimal expansions as rational numbers in fraction form.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Understanding and Applying the Pythagorean Theorem
Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.
8.G.B.6
Understand a proof of the Pythagorean Theorem.
Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
Find missing side lengths involving right triangles and apply to area and perimeter problems.
8.G.B.7
Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).
Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).
Find the distance between points in the coordinate plane using the Pythagorean Theorem.
8.G.B.8
Topic C: Volume and Cube Roots
Define and evaluate cube roots. Solve equations in the form $${x^2=p}$$ and $${x^3=p}$$.
8.EE.A.2 8.NS.A.2
Solve real-world and mathematical problems involving the volume of cylinders and cones.
8.G.C.9
Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free