Find the volume to the nearest whole number.

23. 

    Square base

24. 

    Equilateral base

25. 

    Square base

26. Writing The two cylinders pictured below are congruent. How does the volume of the larger cone compare to the total volume of the two smaller cones? Explain.

    

27. Architecture The Pyramid of Peace is an opera house in Astana, Kazakhstan. The height of the pyramid is approximately 62 m and one side of its square base is approximately 62 m.
    1. What is its volume to the nearest thousand cubic meters?
    2. How tall would a prism-shaped building with the same square base as the Pyramid of Peace have to be to have the same volume as the pyramid?

28. Hardware Builders use a plumb bob to find a vertical line. The plumb bob shown below combines a regular hexagonal prism with a pyramid. Find its volume to the nearest cubic centimeter.

    

29. Reasoning A cone with radius 3 ft and height 10 ft has a volume of 30 π ft 3 . 30 pi , ft cubed , .  What is the volume of the cone formed when the following happens to the original cone?
    1. The radius is doubled.
    2. The height is doubled.
    3. The radius and the height are both doubled.

Algebra Find the value of the variable in each figure. Leave answers in simplest radical form. The diagrams are not to scale.

30. 

    Volume = 18 3 cap volume , equals , 18 square root of 3

31. 

    Volume = 21 π cap volume , equals 21 pi

32. 

    Volume = 24 π cap volume , equals 24 pi

Visualization Suppose you revolve the plane region completely about the given line to sweep out a solid of revolution. Describe the solid.

Then find its volume in terms of π.

33. the y-axis
34. the x-axis

C Challenge

35. the line x = 4 x equals 4
36. the line y = − 1 y equals , minus 1

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