1379 The volume of a sphere is to the volume of the circumscribed cube as is to 6. 1380 The volume of a sphere is to the volume of the inscribed cube as π is to √3. 1381 The volume of a sphere is 120. Find the volume of the circumscribed cube. 1382 The diameter of a sphere is 3 inches. Find the volume of the inscribed cube. 1383 The diameters of two spheres of the same material are a and b respectively. If the first weighs n pounds, find the weight of the second. 1384 The base of a circular cone is equal to a great circle of a sphere, and the altitude of the cone is equal to the diameter of the sphere. Compare their volumes. 1385 Find the volume of a spherical wedge whose angle is 60°, if the radius of the sphere is 5 inches. 1386 The volume of a spherical wedge is 7 cubic feet, and the volume of the sphere is 63 cubic feet. Find the angle of the wedge. 1387 What part of a sphere is a spherical pyramid whose base is a trirectangular triangle? 1388 If the volume of a sphere is 214 cubic inches, what is the volume of a triangular spherical pyramid, the angles of whose base are 80°, 104°, and 116° ? 1389 Find the volume of a spherical sector whose altitude is 7 inches, if the radius of the sphere is 27 inches. 1390 Find the volume of a spherical sector, if the area of its curved surface is 5, and the radius of the sphere is 2. 1391 The radii of the bases of a spherical segment are 7 and 9, and the altitude is 5. Find the volume. 1392 Find the volume of a spherical cone, if the radius of its base is 8, and the radius of the sphere is 10. 1393 If h is the distance of a light from a sphere whose radius is R, 2 π R2h show that the surface illuminated is R+h In the following exercises the earth is considered a perfect sphere, and 8000 miles in diameter, unless otherwise stated. 1394 If a man was 1000 miles above the earth, how much of its surface could he see? 1395 How far above the earth must a man be to see one fifth of its surface ? 1396 A man standing on the sea-shore can see the water of the ocean how far away, if his eye is 6 feet above the level of the sea? 1397 With the eye at the level of the sea, the top of a mast of a ship 200 feet high is just visible on the horizon. What is the distance of the ship from the observer? 1398 Compute the surface and volume of the earth. 1399 The diameter of the sun is about 108.5 times the diameter of the earth. Compare their surfaces and volumes. 1400 The diameter of Jupiter is 11 times that of the earth. Compare their volumes. 1401 The planet Mars has two moons, Deimos and Phobos, whose diameters are estimated to be 7 miles and 6 miles respectively. Compute their surfaces and volumes. 1402 The diameter of the moon is 2163 miles, and the diameter of the earth is 7920 miles. Show that the volume of the moon is almost exactly of the volume of the earth. 1403 Taking the earth's diameter as unity, the diameters of the other major planets are roughly as follows: Mercury, ; Venus, 1; Mars, }; Jupiter, 11; Saturn, 9; Uranus, 4; Neptune, 41. Compare the volume of Jupiter with the combined volumes of all the other major planets. 1404 Assuming that the orbit of the earth around the sun is a circle whose radius is 92,800,000 miles, and assuming that the velocity of the earth in its orbit is uniform, and assuming that the earth completes one revolution around the sun in 365 days, compute the velocity of the earth in its orbit per second. |