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Five-Minute Check (over Lesson 12–2) Then/Now Key Concept: Volume of a Cylinder Example 1: Volume of a Cylinder Example 2: Height of a Cylinder Example 3: Real-World Example: Volume of a Composite Figure Lesson Menu

Find the volume of the figure. A. 80 cm2 B. 85 cm3 C. 400 cm2 D. 400 cm3 5-Minute Check 1

Find the volume of the figure. A. 864 in3 B. 432 in3 C. 216 in3 D. 108 in3 5-Minute Check 2

The volume of a triangular prism is 375 cubic centimeters The volume of a triangular prism is 375 cubic centimeters. The area of the base is 50 square centimeters. What is the height of the prism? A. 0.75 cm2 B. 0.75 cm C. 7.5 cm2 D. 7.5 cm 5-Minute Check 3

A cubic inch of water weighs 0. 036 pound A cubic inch of water weighs 0.036 pound. A 10-gallon fish tank measures 20 inches by 10 inches by 12 inches. How much will the water in the fish tank weigh if it is filled to capacity? A. 86.4 pounds B. 92.1 pounds C. 94.6 pounds D. 2400 pounds 5-Minute Check 4

What is the volume of the house? A. 2,662 m3 B. 10,560 m3 C. 12,870 m3 D. 15,180 m3 5-Minute Check 5

You have already found the areas of circles. (Lesson 11–8) Find the volumes of circular cylinders. Find the volumes of composite figures involving circular cylinders. Then/Now

Concept

A. Find the volume of the cylinder. Round to the nearest tenth. Volume of a Cylinder A. Find the volume of the cylinder. Round to the nearest tenth. V = Bh Volume of a cylinder V = πr2h Replace B with πr2. V ≈ 3.14 ● 72 ● 14 Replace π with 3.14, r with 7, and h with 14. V ≈ 2154.0 Simplify. Answer: The volume is about 2154.0 cubic feet. Example 1 A

Since the diameter is 10 meters, the radius is 5 meters. Volume of a Cylinder B. Find the volume of the cylinder. Round to the nearest tenth. diameter of base 10 m, height 2 m Since the diameter is 10 meters, the radius is 5 meters. V = πr2h Formula for volume of a cylinder V ≈ 3.14 ● 52 ● 2 Replace π with 3.14, r with 5, and h with 2. V ≈ 157 Simplify. Answer: The volume is about 157 cubic meters. Example 1 B

A. Find the volume of the cylinder. Round to the nearest tenth. A. 175.9 in3 B. 336 in3 C. 351.7 in3 D. 615.8 in3 Example 1 CYP A

B. Find the volume of the cylinder with a base diameter of 8 cm and a height of 6 cm. Round to the nearest tenth. A. 1206.4 cm3 B. 301.4 cm3 C. 226.2 cm3 D. 150.8 cm3 Example 1 CYP B

V = Bh Volume of a cylinder V = πr2h Replace B with πr2. Height of a Cylinder The volume of the cylinder is 99 cubic inches. Find the height of the cylinder. Round to the nearest tenth. V = Bh Volume of a cylinder V = πr2h Replace B with πr2. 99 ≈ 3.14 ● 32 ● h Replace V with 99, π with 3.14, and r with 3. Example 2

Answer: The height is about 3.5 inches. Height of a Cylinder 99 ≈ 28.26h Simplify. 3.5 ≈ h Divide each side by 28.26. Answer: The height is about 3.5 inches. Example 2

The volume of a cylinder is 678 cubic inches The volume of a cylinder is 678 cubic inches. Find the height of the cylinder. Round to the nearest tenth. A. 6.0 in. B. 6.4 in. C. 7.2 in. D. 7.5 in. Example 2

Step 1 Find the volume of the prism. Volume of a Composite Figure CAKES A baker designed a wedding cake in the shape shown below. Find the volume of the cake. Step 1 Find the volume of the prism. V = Bh Volume of a prism = 20 ● 20 ● 4 The length and width are 20. The height is 4. = 1600 in3 Multiply. Example 3

Step 2 Find the volume of the cylinder. Volume of a Composite Figure Step 2 Find the volume of the cylinder. V = πr2h Volume of a cylinder ≈ 3.14(5)2(4) Replace r with 5 and h with 4. ≈ 314 in3 Multiply. Step 3 Find the volume of the composite figure. 1600 in3 + 314 in3 = 1914 in3 Answer: The volume of the cake is 1914 in3. Example 3

CAKES A wedding cake has two layers that are cylinders CAKES A wedding cake has two layers that are cylinders. Each layer has a height of 3 inches. The bottom layer has a radius of 12 inches. The upper layer has a radius of 8 inches. What is the volume of the cake? A. 452.16 in3 B. 1959.4 in3 C. 3768 in3 D. 4069.4 in3 Example 3

End of the Lesson