46. Food An ice cream vendor presses a sphere of frozen yogurt into a cone, as shown below. If the yogurt melts into the cone, will the cone overflow? Explain.

    
47. The surface area of a sphere is 5541.77  ft 2 . 5541.77 . ft squared , .  What is its volume to the nearest tenth?
48. Geography The circumference of Earth at the equator is approximately 40,075 km. About 71% of Earth is covered by oceans and other bodies of water. To the nearest thousand square kilometers, how much of Earth's surface is land?

Find the surface area and volume of each figure.

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52. Astronomy The diameter of the Earth is about 7926 mi. The diameter of the moon is about 27% of the diameter of Earth. What percent of the volume of Earth is the volume of the moon? Round your answer to the nearest whole percent.
53. Science The density of steel is about 0.28  lb  / in . 3 . 0.28 , lb , slash . in , . cubed , .  Could you lift a solid steel ball with radius 4 in.? With radius 6 in.? Explain.

54. A cube with edges 6 in. long fits snugly inside a sphere as shown below. The diagonal of the cube is the diameter of the sphere.

    

    1. Find the length of the diagonal and the radius of the sphere. Leave your answer in simplest radical form.
    2. What is the volume of the space between the sphere and the cube to the nearest tenth?

C Challenge

Find the radius of a sphere with the given property.

55. The number of square meters of surface area equals the number of cubic meters of volume.
56. The ratio of surface area in square meters to volume in cubic meters is 1 : 5.
57. Suppose a cube and a sphere have the same volume.
    1. Which has the greater surface area? Explain.
    2. Writing Explain why spheres are rarely used for packaging.
58. A plane intersects a sphere to form a circular cross section. The radius of the sphere is 17 cm and the plane comes to within 8 cm of the center. Draw a sketch and find the area of the cross section, to the nearest whole number.

59. History below, the sphere fits snugly inside the cylinder. Archimedes (about 287–212 b.c.) requested that such a figure be put on his gravestone along with the ratio of their volumes, a finding that he regarded as his greatest discovery. What is that ratio?

    

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