Volumes of Prisms and Cylinders LESSON 12–4

Lesson Menu Five-Minute Check (over Lesson 12–3) TEKS Then/Now Key Concept : Volume of a Prism Example 1: Volume of a Prism Key Concept: Volume of a Cylinder Example 2: Volume of a Cylinder Key Concept: Cavalieri’s Principle Example 3: Volume of an Oblique Solid Example 4: Comparing Volumes of Solids

Over Lesson 12–3 5-Minute Check 1 A.600 in 2 B in 2 C in 2 D in 2 Find the surface area of the regular pyramid.

Over Lesson 12–3 5-Minute Check 2 A ft 2 B ft 2 C ft 2 D ft 2 Find the surface area of the cone.

Over Lesson 12–3 5-Minute Check 3 A.420 ft 2 B.480 ft 2 C ft 2 D.710 ft 2 Find the surface area of the regular pyramid.

Over Lesson 12–3 5-Minute Check 4 A m 2 B m 2 C m 2 D m 2 Find the surface area of the cone.

Over Lesson 12–3 5-Minute Check 5 A.80 ft 2 B.200 ft 2 C.240 ft 2 D.260 ft 2 Find the surface area of a square pyramid with base length of 10 feet and slant height of 8 feet.

Over Lesson 12–3 5-Minute Check 6 A cm 2 B cm 2 C cm 2 D cm 2 Find the lateral area of a cone with a diameter length of 10 centimeters and a slant height of 13 centimeters. Round your answer to the nearest tenth.

TEKS Targeted TEKS G.10(B) Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change. G.11(D) Apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. Mathematical Processes G.1(D), G.1(E)

Then/Now You found surface areas of prisms and cylinders. Find volumes of prisms. Find volumes of cylinders.

Concept

Example 1 Volume of a Prism Answer: The volume of the prism is 1500 cubic centimeters. V BhVolume of a prism 1500Simplify. Find the volume of the prism.

Example 1 A.6480 in 3 B.8100 in 3 C.3240 in 3 D.4050 in 3 Find the volume of the prism.

Concept

Example 2 Volume of a Cylinder Find the volume of the cylinder to the nearest tenth. Answer: The volume is approximately 18.3 cm 3. Volume of a cylinder ≈18.3Use a calculator. = (1.8) 2 (1.8)r = 1.8 and h = 1.8

Example 2 A.62.8 cm 3 B cm 3 C cm 3 D cm 3 Find the volume of the cylinder to the nearest tenth.

Concept

Example 3 Volume of an Oblique Solid Find the volume of the oblique cylinder to the nearest tenth. To find the volume, use the formula for a right cylinder. Answer: The volume is approximately 17,671.5 cubic feet. Volume of a cylinder Use a calculator. r 15, h 25

Example 3 A cm 3 B.16,725.8 cm 3 C.5324 cm 3 D cm 3 Find the volume of the oblique cylinder to the nearest tenth.

Example 4 Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than the volume of Prism A, what is the length of each prism? A12B8 C4D3.5 Prism APrism B Comparing Volumes of Solids

Example 4 Read the Item You know the volume of each solid and that the difference between their volumes is 128 cubic inches. Solve the Item Volume of Prism B – Volume of Prism A=128Write an equation. 4x ● 9 – 4x ● 5=128Use V = Bh. 16x=128Simplify. x=8Divide each side by 16. Answer: The length of each prism is 8 inches. The correct answer is B. Comparing Volumes of Solids

Example 4 A.4 in. B.6 in. C.8 in. D.10.5 in. Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 192 cubic inches greater than the volume of Prism A, what is the length of each prism? Prism A Prism B

Volumes of Prisms and Cylinders LESSON 12–4