1. Five-Minute Check (over Lesson 11–1) Mathematical Practices 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: Standardized Test Example: Comparing Volumes of Solids
Lesson Menu

2. Which three-dimensional shape can be generated by rotating a two-dimensional shape around an axis?
A. cone
B. pyramid
C. rectangular prism
D. triangular prism
5-Minute Check 1

3. Which three-dimensional shape can be generated by rotating a square around a horizontal axis?
A. cone
B. cube
C. cylinder
D. square pyramid
5-Minute Check 2

4. What is the shape of the cross section of the cone if it is cut vertically?
A. circle
B. triangle
C. rhombus
D. trapezoid
5-Minute Check 3

5. What is the shape of the cross section of the cylinder if it is cut horizontally?
A. circle
B. triangle
C. rhombus
D. trapezoid
5-Minute Check 4

6. Which cross section is not possible by intersecting the rectangular pyramid by a plane?
A. rectangle
B. triangle
C. trapezoid
D. pentagon
5-Minute Check 5

7. 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.
A cm2
B cm2
C cm2
D cm2
5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
7 Look for and make use of structure.
Content Standards
G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. MP

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

10. Concept

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

12. Find the volume of the prism.
A in3
B in3
C in3
D in3
Example 1

13. Concept

14. Find the volume of the cylinder to the nearest tenth.
Volume of a Cylinder
Find the volume of the cylinder to the nearest tenth.
Volume of a cylinder
= (1.8)2(1.8) r = 1.8 and h = 1.8
≈ 18.3 Use a calculator.
Answer: The volume is approximately 18.3 cm3.
Example 2

15. Find the volume of the cylinder to the nearest tenth.
A cm3
B cm3
C cm3
D cm3
Example 2

16. Concept

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

18. Find the volume of the oblique cylinder to the nearest tenth.
A cm3
B. 16,725.8 cm3
C cm3
D cm3
Example 3

19. Comparing Volumes of Solids
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 height of each prism?
Prism A
Prism B
A 12 B 8
C 4 D 3.5
Example 4

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

21. Prisms A and B have the same width and height, but different lengths
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?
A. 4 in.
B. 6 in.
C. 8 in.
D in.
Prism A
Prism B
Example 4