Mathematics
Grade 10
15 min
Volume of prisms and cylinders
Volume of prisms and cylinders
What you'll learn
- Identify and plot at least 8 out of 10 points correctly on a coordinate plane, given their ordered pairs (x, y).
- Follow a set of 5 multi-step directions to move a point on a coordinate plane and accurately state the final coordinates of the point.
- Explain in your own words how the x-coordinate and y-coordinate determine the location of a point on a coordinate plane.
- Apply knowledge of coordinate planes to create a simple path (at least 4 segments) on a grid, listing the ordered pairs needed to define the path.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Define volume and identify the base and height of various prisms and cylinders.
State and apply the general formula for the volume of a right prism (V = B * h).
State and apply the specific formula for the volume of a cylinder (V = π * r^2 * h).
Calculate the volume of composite solids composed of prisms and cylinders.
Solve problems to find a missing dimension (e.g., height, radius) of a prism or cylinder given its volume.
Apply volume formulas to solve real-world application problems.
Ever wonder how much soda fits in a can or how much water is needed to fill a swimming pool? 🏊♀️ That's all about calculating volume!
Volume measures the amount of three-dimensional space an object occupies. In this tutorial, you will master the single, powerful fo...
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Key Concepts & Vocabulary
TermDefinitionExample
VolumeThe amount of three-dimensional space an object occupies, measured in cubic units (like cm³, m³, or in³).A cube with side lengths of 1 cm has a volume of 1 cubic centimeter (1 cm³).
PrismA three-dimensional solid with two identical, parallel polygon faces called bases. The other faces are rectangles that connect the corresponding sides of the bases.A standard cardboard box is a rectangular prism. A Toblerone box is a triangular prism.
CylinderA three-dimensional solid with two identical, parallel circular bases and one curved lateral surface connecting them.A can of soup or a roll of paper towels.
Base (of a Prism or Cylinder)One of the two parallel, congruent faces that define the shape. The shape of the base gives the prism its name (e.g., a triangular base m...
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Core Formulas
General Formula for Volume of Prisms and Cylinders
V = B \cdot h
This is the fundamental formula. The Volume (V) of any right prism or cylinder is found by multiplying the Area of its Base (B) by its perpendicular height (h).
Volume of a Rectangular Prism
V = l \cdot w \cdot h
This is a specific version of the general formula where the base is a rectangle. The base area (B) is calculated as length (l) times width (w).
Volume of a Cylinder
V = \pi r^2 h
This is a specific version of the general formula where the base is a circle. The base area (B) is calculated as pi (π) times the radius (r) squared.
4 more steps in this tutorial
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Challenging
The volume of a cylinder is 401.92 cubic units. Its height is exactly twice its radius. What is the radius of the cylinder? Use π ≈ 3.14.
A.2 units
B.4 units
C.8 units
D.16 units
Challenging
A concrete pipe is a hollow cylinder with an outer radius of 30 cm, an inner radius of 25 cm, and a length (height) of 200 cm. What is the volume of the concrete used to make the pipe? Use π ≈ 3.14.
A.17,270 cm³
B.157,000 cm³
C.172,700 cm³
D.565,200 cm³
Challenging
A cylindrical swimming pool has a diameter of 8 meters and a height of 1.5 meters. If water is pumped into the pool at a rate of 5 cubic meters per minute, approximately how long will it take to fill the pool? Use π ≈ 3.14.
A.7.5 minutes
B.15 minutes
C.30 minutes
D.60 minutes
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Frequently asked questions
What grade level is "Volume of prisms and cylinders"?
Volume of prisms and cylinders is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Volume of prisms and cylinders?
You'll be able to: Identify and plot at least 8 out of 10 points correctly on a coordinate plane, given their ordered pairs (x, y); Follow a set of 5 multi-step directions to move a point on a coordinate plane and accurately state the final….
Is "Volume of prisms and cylinders" 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 Volume of prisms and cylinders?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.