Mathematics
Grade 10
15 min
Solids of revolution
Solids of revolution
What you'll learn
- Solve multiplication problems involving fractions and whole numbers where the whole number is less than 10, by representing the problem as repeated addition (e.g., 3 x 1/4 = 1/4 + 1/4 + 1/4) and writing the correct answer.
- Explain, using pictures or words, why multiplying a fraction by a whole number results in a fraction or a whole number greater than the original fraction (if the whole number is greater than 1).
- Apply the concept of multiplying a fraction by a whole number to solve 3 out of 4 word problems involving real-world scenarios.
- Identify the correct multiplication expression needed to solve a word problem involving repeated addition of fractions, given 3 different multiplication expressions.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the three-dimensional solid (cylinder, cone, sphere) generated by revolving a two-dimensional shape (rectangle, right triangle, semicircle).
Determine the dimensions (radius, height) of a solid of revolution based on the original two-dimensional shape and the axis of revolution.
Visualize and sketch the resulting solid of revolution.
Apply the correct formulas to calculate the volume of cylinders, cones, and spheres.
Apply the correct formulas to calculate the surface area of cylinders, cones, and spheres.
Solve problems by working backwards from a given volume or surface area to find a missing dimension.
Ever wonder how a potter on a wheel can turn a lump of clay into a perfectly symmetrical vase? 🏺 You're about to learn the mathematical s...
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Key Concepts & Vocabulary
TermDefinitionExample
Solid of RevolutionA three-dimensional figure formed by rotating a two-dimensional shape around a fixed line.Rotating a rectangle around one of its sides creates a cylinder.
Axis of RevolutionThe fixed line that a two-dimensional shape is rotated around to create a solid of revolution.If you spin a right triangle around one of its legs, that leg is the axis of revolution.
Generating RegionThe two-dimensional shape that is rotated to form the solid of revolution.A semicircle is the generating region for a sphere.
Cylinder (as a solid of revolution)A solid formed by revolving a rectangle about one of its sides.A 5x3 rectangle revolved around the side of length 5 creates a cylinder with a height of 5 and a radius of 3.
Cone (as a solid of revolution)A solid formed by re...
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Core Formulas
Volume of a Cylinder
V = \pi r^2 h
Use this formula to find the volume of a cylinder, where 'r' is the radius of the circular base and 'h' is the height of the cylinder.
Volume of a Cone
V = \frac{1}{3} \pi r^2 h
Use this formula to find the volume of a cone. Notice it is exactly one-third the volume of a cylinder with the same radius 'r' and height 'h'.
Volume of a Sphere
V = \frac{4}{3} \pi r^3
Use this formula to find the volume of a sphere, where 'r' is the radius of the sphere.
Surface Area of a Cylinder
SA = 2\pi rh + 2\pi r^2
Use this formula to find the total surface area of a cylinder. The first part (2πrh) is the area of the curved side, and the second part (2πr²) is the area of the two circular base...
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Challenging
A cone is generated by revolving a right triangle with legs 5 cm and 12 cm around the 12 cm leg. A cylinder is generated by revolving a 5 cm by 12 cm rectangle around the 12 cm side. What is the ratio of the cone's volume to the cylinder's volume?
A.1:1
B.3:1
C.1:3
D.2:3
Challenging
A solid metal sphere with a volume of 288π cm³ is melted down and recast into a cone with a radius of 6 cm. What is the height of the cone?
A.12 cm
B.18 cm
C.36 cm
D.24 cm
Challenging
The region bounded by the vertical lines x=3, x=7 and the horizontal lines y=0, y=10 is revolved around the y-axis. What is the volume of the resulting solid?
A.160π
B.400π
C.290π
D.490π
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Frequently asked questions
What grade level is "Solids of revolution"?
Solids of revolution is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Solids of revolution?
You'll be able to: Solve multiplication problems involving fractions and whole numbers where the whole number is less than 10, by representing the problem as repeated addition (e.g., 3 x 1/4 = 1/4 + 1/4 + 1/4) and writing the correct answer….
Is "Solids of revolution" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Solids of revolution?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.