Page 53 - Math Course 3 (Book 2)

Geometric Surface Area: Cones

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1
Let’s Begin 2 in. r = 1 in.
2
4

Lateral Area of a Cone

Example 8 in. h = 8 in.

Ice cream

A sugar cone has an altitude of 8 inches and a
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diameter of 2 inches. Find the lateral area of the
2
sugar cone. Answer The lateral area is approximately
31.8 square inches.
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Explore 2 in.
We are given the altitude and 2
the diameter of the base. We
need to find the slant height of
the cone. Surface Area of the Cone

Plan 8 in.
The radius of the base, height, and Example
slant height form a right triangle.
Use the Pythagorean Theorem to
solve for the slant height. Then use Find the surface area of the cone. Round to the
the formula for the lateral area of a nearest tenth.
right circular cone.
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Solve r = 1 in.
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Write an equation and solve for . 3.2 cm
Pythagorean 1.4 cm
² = 1.25² + 8²
Theorem
² = 65.5625 Simplify. h = 8 in.

≈ 8.1 Take the square T = πr + πr² Surface area of a cone
root of each side.

Next, use the formula for the lateral area of = π(1.4)(3.2) + π(1.4)² r = 1.4, = 3.2
a right circular cone.
≈ 20.2 Use a calculator.

L = πr Lateral area of a cone
The surface area is approximately
Answer
≈ π(1.25)(8.1) r = 1.25, ≈ 8.1 20.2 square centimeters.
Use a
≈ 31.8
calculator.
Check
Use estimation to check the reasonableness of this
result. The lateral area is approximately 3 • 1.25 • 8
or 30 square inches. Compared to the estimate, the
answer is reasonable.

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