31. Suppose that a cylinder has a radius of r units, and that the height of the cylinder is also r units. The lateral area of the cylinder is 98 π 98 pi square units.
    1. Algebra Find the value of r.
    2. Find the surface area of the cylinder.
32. Geometry in 3 Dimensions Use the diagram below.

    

    1. Find the three coordinates of each vertex A, B, C, and D of the rectangular prism.
    2. Find AB.
    3. Find BC.
    4. Find CD.

    5. Find the surface area of the prism.

Visualization Suppose you revolve the plane region completely about the given line to sweep out a solid of revolution. Describe the solid and find its surface area in terms of π . pi .

33. the y-axis
34. the x-axis
35. the line y = 2 y equals 2
36. the line x = 4 x equals 4
37. Reasoning Suppose you double the radius of a right cylinder.
    1. How does that affect the lateral area?
    2. How does that affect the surface area?
    3. Use the formula for surface area of a right cylinder to explain why the surface area in part (b) was not doubled.

38. Packaging Some cylinders have wrappers with a spiral seam. Peeled off, the wrapper has the shape of a parallelogram. The wrapper for a biscuit container has base 7.5 in. and height 6 in.

    

    1. Find the radius and height of the container.
    2. Find the surface area of the container.

C Challenge

What is the surface area of each solid in terms of π ? pi question mark

39. 
    Image Long Description
40. 
41. 

42. Each edge of the large cube below is 12 inches long. The cube is painted on the outside, and then cut into 27 smaller cubes. Answer these questions about the 27 cubes.

    

    1. How many are painted on 4, 3, 2, 1, and 0 faces?
    2. What is the total surface area that is unpainted?
43. Algebra The sum of the height and radius of a cylinder is 9 m. The surface area of the cylinder is 54 π   m 2 . 54 pi , m squared , . Find the height and the radius.

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