Ex. 208. Find an expression for the altitude of a zone whose area is A on a sphere whose volume is V.

Ex. 209. Assuming the atmosphere to extend to a height of 50 miles above the earth's surface and the earth to be a sphere whose radius is approximately 4000 miles, what is the volume of the atmosphere ?

Ex. 210. Assuming the earth to be a sphere whose radius is approximately 4000 miles, how far at sea is a lighthouse visible, if it is 80 ft. high? Ex. 211. A swimmer, whose eye is at the surface of the water, can just see the top of a buoy a mile distant. If the buoy is 8 in. out of the water, what is the radius of the earth?

Ex. 212. How high above the surface of the earth must a man be in 1

in order that he may see

n

of it?

Ex. 213. What is the area of the zone illuminated by a taper h decimeters from the surface of a sphere whose radius is r decimeters ?

Ex. 214. In a cube whose edge is 1 ft. there are inscribed a cylinder, a cone, a sphere, and a square pyramid. What is the volume of each of these solids ?

Ex. 215. A cylindrical boiler with hemispherical ends has a total length of 12 ft. and its circumference is 10 ft. What is its surface? What weight of water is required to fill it?

Ex. 216. Find the diameter of a sphere which is circumscribed about a regular square pyramid whose base is 4 in. square and altitude 8 in.

Ex. 217. A sphere 8 in. in diameter has a 3-inch hole bored through its center. What is the remaining volume ?

Ex. 218. What is the volume of the portion of a sphere lying outside of an inscribed cylinder of revolution whose altitude is h and radius r?

Ex. 219. Inscribe a circle in a given spherical triangle.

Ex. 220. Find the locus of the centers of the sections of a given sphere made by planes passing through a given straight line.

Ex. 221. Find the locus of the centers of the sections of a given sphere made by planes passing through a given point without the sphere.

Ex. 222. Having given the radius, construct a spherical surface to pass through three given points.

Ex. 223. Having given the radius, construct a spherical surface to pass through two given points and be tangent to a given plane or to a given sphere.

Ex. 224. Having given the radius, construct a spherical surface to pass through a given point and be tangent to two given planes.

Ex. 225. Having given the radius, construct a spherical surface to be tangent to three given planes.

100 Sq. Millimeters (8q mm) = 1 Sq. Centimeter (8q cm)

1000 Cu. Millimeters (cu mm) 1 Cu. Centimeter (cu cm)

The liter contains a volume equal to a cube whose edge is a decimeter.

The weight of a gram is the weight of a cubic centimeter of distilled water at its greatest density.

NOTES.1. The specific gravity of a substance (solid or liquid) is the ratio between the weight of any volume of the substance and the weight of a like volume of distilled water at its greatest density; consequently, since a cubic centimeter of distilled water at its greatest density weighs one gram, the weight of any substance may be found if its specific gravity and volume are known.

2. A cubic foot of water weighs 621 lb., or 1000 oz.

3. A bushel contains 2150.42 cu. in.

4. A gallon contains 231 cu. in.