Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 14
Math
Unit 7
8th Grade
Lesson 14 of 16
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Solve real-world and mathematical problems involving the volume of cylinders and cones.
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
Throughout the next few lessons, students will be working with some familiar and new formulas for volume. From sixth and seventh grades, students should be familiar with formulas for the area and circumference of circles, and the area and volume of 2-D and 3-D figures composed of polygons. Consider setting up a space, visually accessible to all students, where these formulas can be displayed in the classroom as they come up. Students can also create their own reference sheets with the formulas for them to keep in their own materials (MP.5).
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
A pentagonal prism and a cylinder are shown below. Use the measurements given to determine the volume of each figure.
Area of pentagonal base: $$27\space \mathrm{u}^2$$
Height of prism: $$6.2 \space \mathrm{u}$$
Volume: __________
Area of circular base: $$16\space \mathrm{u}^2$$
Height of cylinder: $$5.8 \space \mathrm{u}$$
a. A cylindrical can of cranberry sauce measures $$3$$ inches in diameter and $${4{7\over{16}}}$$ inches in height. What is the volume of the can? Give your answer to the nearest tenth of a cubic inch.
b. A different brand of cranberry sauce also comes in a cylindrical can and has a volume of $$50\space\mathrm{in}^3$$. The can has a height of $${5.5}$$ inches. What is the radius of the can? Give your answer to the nearest tenth of an inch.
Watch this video, "How Many Cones Does it Take to Fill a Cylinder with the Same Base and Height".
a. What is the relationship between the volume of a cylinder and the volume of a cone with the same base and height?
b. The cylinder and cone below have congruent bases and the same height.
Grade 8 Unit 5 Lesson 15 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed April 7, 2018, 10:08 a.m..
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
In pottery class, Asher and Brandi make three-dimensional solid shapes out of clay.
a. Asher makes a cylinder with a radius of $$3$$ inches and a height of $${6 {1\over2}}$$ inches. How many cubic inches of clay did Asher use?
b. Brandi makes a cone and uses approximately $$64 \space \mathrm{in}^3$$ of clay. The height of Brandi’s cone is $$4$$ inches. What is the radius of the circular base of Brandi’s cone?
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 13
Lesson 15
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.
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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
8.G.C.9
Solve real-world and mathematical problems involving the volume of spheres.
Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.
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