Surface Area of Cylinders - Lesson 10.2 - Lateral and Total Surface Area

Sep 18, 2026

Uploaded by Aurelia

Lesson focuses on finding the surface area of a cylinder by modeling its curved lateral surface and its two circular bases. It connects formulas for circumference, lateral area, and total surface area, explaining how nets can unfold into a rectangle to match dimensions. Worked examples compute lateral and total areas using given radii, heights, and π = 3.14, then practice problems require rounding to the nearest tenth or whole number. Real-world applications include labels and metal coverings for cans.

LanguageEnglish

CategoryExam

FormatPDF

Pages6

Reading Time15 min

AccessFree to download

Lesson 10.2: Surface Area of Cylinders

Modeling the Surface Area

Lateral and Total Surface Area Formulas

Finding Surface Area in Real-World Situations

Guided Practice

Independent Practice

How do you find the surface area of a cylinder? ESSENTIAL QUESTION LESSO N Surface Area of Cylinders Expressions, equations, and relationships—8.7.B … make connections to the formulas for lateral and total surface area and determine solutions for problems involving…cylinders. Modeling the Surface Area of a Cylinder Just as you did with a prism, you can use a net to help you find a formula for the surface area of a cylinder. The lateral area of a cylinder is the area of the curved surface that connects the two bases. The net shows that the lateral surface is a rectangle. Use the diagram of the oatmeal container and its net. Imagine unrolling the container’s lateral surface to form a rectangle. What dimension of the cylinder matches the rectangle’s length? What dimension of the cylinder matches the rectangle’s height? Express the lateral area of a cylinder in words and as a formula using the given variables. Lateral area = Area of one = Length · Height L = (C = circumference, h = height) L = (r = radius, h = height) Express the total surface area of a cylinder in words and as a formula using the given variables. Total surface area = Area of two + Area of one S = (B = base area, C = circumference, h = height) S = (r = radius, h = height) Reflect 1. Communicate Mathematical Ideas How is the process for finding lateral and total surface area of a cylinder like the process for a prism? r r C = 2πr ℓ = 2πr A B The formula for the circumference of acircle is C = 2πr. C Lesson 10.2 275 © Houghton Mifflin Harcourt Publ ishing Company My Notes 4 ft 7 ft 6 cm 2. L: 7 ft Finding the Surface Area of a Cylinder The total surface area of a cylinder is the area of the bases plus the lateral area. Find the lateral and total surface area of the cylinder to the nearest tenth. Use 3.14 for π. Find the lateral area. L = 2πrh ≈ 2(3.14)(4)(7) ≈ 175.84 The lateral area is about 175.8 square feet. surface area. Find the total S = 2πr2 + L ≈ 2(3.14)(42) + ≈ 100.48 + ≈ 276.32 The total surface 175.84 175.84 area of the cylinder is about 276.3 square feet. Find the lateral and total surface area of each cylinder. Round your answers to the nearest tenth. Use 3.14 for π. 3. L: Use the formula for the lateral area of a cylinder. Substitute. Simplify. Use the formula for the total surface area of a cylinder. Substitute. Simplify. Add. EXAMPLE 1 8.7.B STEP 1 STEP 2 Lateral and Total Surface Area of a Cylinder The lateral area L of a cylinder with height h and radius r is the circumference of the base times the height. L = Ch or L = 2πrh The total surface area S of a cylinder with height h and radius r is twice the area of a base B plus the lateral area L. S = 2B + L or S = 2πr2 + 2πrh Radius Base Height © Houghton Mifflin Harcourt Publishing Company 276 Unit 3 © Houghton Mifflin Harcourt Publishing Company Finding the Surface Area of a Cylinder in a Real-World Situation You can find many examples of cylinders in your kitchen. The can shown is 11 inches high and has a diameter of 9 inches. How many square inches of paper are needed for the label? How many square inches of metal are needed to make the entire can? Round your answers to the nearest whole number. Use 3.14 for π. Find the radius of the base. d = 9 in., so r = 4.5 in. To find the area of the label, find the lateral area. L = 2πrh ≈ 2(3.14)(4.5)(11) ≈ 310.86 It takes about 311 square inches of paper to make the label. To find the amount of metal, find the total surface area. S = 2πr2 + 2πrh ≈ 2(3.14)(4.52) + 2(3.14)(4.5)(11) ≈ 127.17 + 310.86 ≈ 438.03 It takes about 438 square inches of metal to make the can. EXAMPLE 2 ~~ ~~ 8.7. B The radius is half of the diameter. Use the formula for the lateral area of a cylinder. Substitute. Multiply. Use the formula for the total surface area of a cylinder. Substitute. Simpl

FAQs

How do you find the lateral area of a cylinder?

Compute the circumference of the base times the cylinder’s height: L = Ch or L = 2πrh.

How do you find the total surface area of a cylinder?

Add the areas of the two bases and the lateral area: S = 2B + L or S = 2πr² + 2πrh.

Why is a net helpful for finding cylinder surface area?

Unrolling the lateral surface forms a rectangle whose length matches the cylinder’s circumference and whose height matches the cylinder’s height, making the lateral area formula clear.

Sep 18, 2026

Uploaded by Aurelia