Mathematics
Grade 10
15 min
Surface area of prisms and cylinders
Surface area of prisms and cylinders
What you'll learn
- Identify the x-axis and y-axis on a coordinate plane with 100% accuracy.
- Explain how to locate a point on a coordinate plane using its ordered pair (x, y) to another student.
- Apply the concept of ordered pairs to accurately plot at least 4 out of 5 points on a coordinate plane.
- Determine the ordered pair (x,y) for 3 out of 4 pre-plotted points on a coordinate plane.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the bases, height, and lateral surfaces of various prisms and cylinders.
Differentiate between lateral surface area and total surface area.
Derive and apply the general formula for the surface area of a right prism (SA = 2B + Ph).
Derive and apply the formula for the surface area of a right cylinder (SA = 2πr² + 2πrh).
Calculate the surface area of composite figures involving prisms and cylinders.
Solve real-world problems involving the surface area of prisms and cylinders.
Ever wondered exactly how much wrapping paper you need for a gift, or how much paint is required to cover a cylindrical water tank? 🎁
This tutorial will guide you through calculating the surface area—the total area of the outside of a 3D object—for two common shapes: prisms...
2
Key Concepts & Vocabulary
TermDefinitionExample
PrismA three-dimensional solid with two parallel and congruent polygonal faces called bases. Its other faces, called lateral faces, are parallelograms (and rectangles in a right prism).A standard cardboard box is a rectangular prism. A tent can be a triangular prism.
CylinderA three-dimensional solid with two parallel, congruent circular bases and a curved lateral surface connecting them.A can of soup or a paper towel roll.
NetA two-dimensional pattern that can be folded to create a three-dimensional figure. Visualizing the net helps in understanding all the surfaces that contribute to the total area.The net of a cylinder is two circles and one rectangle.
Lateral Surface Area (LSA)The sum of the areas of the lateral faces or surfaces of a 3D object, excluding the are...
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Core Formulas
Surface Area of a Right Prism
SA = 2B + Ph
This formula calculates the total surface area of any right prism. 'B' is the area of one base, 'P' is the perimeter of that base, and 'h' is the height of the prism (the distance between the bases). The term 'Ph' calculates the lateral surface area.
Surface Area of a Right Cylinder
SA = 2πr² + 2πrh
This formula calculates the total surface area of a right cylinder. 'r' is the radius of the circular base and 'h' is the height of the cylinder. The term '2πr²' is the area of the two circular bases, and '2πrh' is the lateral surface area.
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Challenging
A company wants to manufacture a cylindrical can with a fixed volume of 54π cubic inches. To minimize material costs, the surface area must be minimized. Which of the following dimensions for radius (r) and height (h) achieves this?
A.r = 2 in, h = 13.5 in
B.r = 3 in, h = 6 in
C.r = 6 in, h = 1.5 in
D.r = 1 in, h = 54 in
Challenging
If the radius of a cylinder is doubled and its height is halved, which statement is true about the new total surface area (SA') compared to the original (SA)?
A.SA' is always smaller than SA.
B.SA' is always equal to SA.
C.SA' is always larger than SA.
D.The relationship depends on the initial ratio of r to h.
Challenging
A rectangular prism with dimensions 10cm x 10cm x 20cm has a cylinder with a radius of 2cm drilled completely through the center of its 10x10 bases. What is the total surface area of the resulting object? (Leave your answer in terms of π).
A.1000 + 80π
B.1000 - 8π
C.1000 + 76π
D.1000 + 72π
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Frequently asked questions
What grade level is "Surface area of prisms and cylinders"?
Surface area of prisms and cylinders is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Surface area of prisms and cylinders?
You'll be able to: Identify the x-axis and y-axis on a coordinate plane with 100% accuracy; Explain how to locate a point on a coordinate plane using its ordered pair (x, y) to another student; Apply the concept of ordered pairs to accurately plot….
Is "Surface area 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 Surface area of prisms and cylinders?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.