Mathematics
Grade 10
15 min
Volume of pyramids and cones
Volume of pyramids and cones
What you'll learn
- Identify the coordinates (x, y) of at least 8 out of 10 objects placed on a coordinate plane that includes all four quadrants.
- Plot at least 7 out of 10 points correctly on a coordinate plane with all four quadrants, given their coordinates (x, y).
- Explain, using at least three sentences, how the signs (+/-) of the x and y coordinates determine which quadrant a point is located in.
- Determine the distance between two points on the coordinate plane that share the same x or y coordinate, and explain the process used.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Recall and correctly apply the formulas for the volume of a pyramid and a cone.
Calculate the volume of a right pyramid given its base dimensions and perpendicular height.
By the end of of this lesson, students will be able to calculate the volume of a right cone given its radius and perpendicular height.
Differentiate between perpendicular height and slant height and identify which is used for volume calculations.
Use the Pythagorean theorem to find the perpendicular height when given the slant height and a base dimension (like radius).
Solve for a missing dimension (height, radius, or base length) when the volume is provided.
Explain the relationship between the volume of a pyramid/cone and a prism/cylinder with the same base and height.
Ever wondered...
2
Key Concepts & Vocabulary
TermDefinitionExample
PyramidA three-dimensional solid with a polygon base and triangular faces that meet at a single point called the apex.The Great Pyramid of Giza has a square base and four triangular faces.
ConeA three-dimensional solid with a circular base and a single curved surface that tapers to a point called the apex.An ice cream cone or a standard traffic cone.
ApexThe highest point or vertex of a pyramid or cone, opposite the base.The sharp tip of a cone.
Base Area (B)The area of the polygon or circle that forms the bottom of the pyramid or cone. The formula for B depends on the shape of the base.For a square pyramid with a side length of 5 cm, the Base Area (B) is 5 cm * 5 cm = 25 cm².
Perpendicular Height (h)The straight-line distance from the apex to the center of the base,...
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Core Formulas
Volume of a Pyramid
V = \frac{1}{3} B h
Use this formula to find the volume (V) of any pyramid. 'B' represents the area of the pyramid's base (e.g., for a square base, B = side²), and 'h' is the perpendicular height from the apex to the base.
Volume of a Cone
V = \frac{1}{3} \pi r^2 h
Use this formula to find the volume (V) of a cone. 'r' is the radius of the circular base, and 'h' is the perpendicular height. Note that \pi r^2 is the formula for the area of the circular base (B).
The 1/3 Relationship
Volume_{Pyramid/Cone} = \frac{1}{3} Volume_{Prism/Cylinder}
The volume of a pyramid or cone is exactly one-third the volume of a prism or cylinder that has the same base area and the same perpendicular height. This is why the...
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Challenging
A square pyramid has a slant height of 13 feet and a perpendicular height of 12 feet. What is its volume?
A.200 ft³
B.400 ft³
C.500 ft³
D.600 ft³
Challenging
A cone is carved from a solid cube with a side length of 10 cm. The cone has the largest possible base and height that can fit in the cube. What is the ratio of the cone's volume to the cube's volume?
A.π / 12
B.π / 6
C.π / 4
D.π / 3
Challenging
Two cones, A and B, have equal volumes. Cone A has radius 'r' and height 'h'. Cone B has a radius of '2r'. What is the height of Cone B in terms of 'h'?
A.h / 2
B.2h
C.h / 4
D.4h
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Frequently asked questions
What grade level is "Volume of pyramids and cones"?
Volume of pyramids and cones is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Volume of pyramids and cones?
You'll be able to: Identify the coordinates (x, y) of at least 8 out of 10 objects placed on a coordinate plane that includes all four quadrants; Plot at least 7 out of 10 points correctly on a coordinate plane with all four quadrants, given their….
Is "Volume of pyramids and cones" 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 pyramids and cones?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.