Ex. 1248. A lune whose angle is equal to 40° is equivalent to a zone on the same sphere. Find the ratio of the altitude of the zone to the radius

of the sphere.

Ex. 1249. The diedral angles of a spherical pyramid of six sides are 140°. Find the volume of the pyramid if the radius is equal to 10.

Ex. 1250. Through a sphere whose diameter is 10 m. a cylindrical hole of 5 m. diameter is bored. Find the volume of the solid if the axis of the cylinder passes through the center of the sphere.

Ex. 1251. The surface of a sphere is equivalent to the lateral surface of the circumscribed cylinder.

Ex. 1252. Two bi-rectangular spherical triangles are equal if the oblique angles are equal.

Ex. 1253. Find the ratio of a sphere to its circumscribed cube.

Ex. 1254. The area of a zone on a sphere is 20, its altitude 4. Find the radius of the sphere.

Ex. 1255. If the diagonals of a spherical quadrilateral bisect each other, the opposite sides are equal.

Ex. 1256. The radius of a sphere is 9 in. Find the volume of a spherical wedge whose angle is equal to 60°.

Ex. 1257. Find the radius of a sphere equivalent to a cone of revolution, the radius of whose base is equal to r and whose altitude is equal to h.

Ex. 1258. The area of a zone is equal to A, its altitude is equal to h. Find the radius of the sphere.

Ex. 1259. The volume of a sphere is numerically equal to one-half its surface. Find the radius.

Ex. 1260. The volume of a cylinder of revolution is equal to one-half the product of its lateral surface by the radius of its base.

Ex. 1261. How many square miles of the surface of the earth can be seen from a point 1000 miles above the surface, if the earth is supposed to be a perfect sphere whose radius is equal to 4000 miles?

Ex. 1262. If from a point without a sphere a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.

Ex. 1263. If through the line of intersection of two spheres a plane be passed, tangents from a point of the plane to the spheres are equal.

Ex. 1264. The radius of a sphere is r, the area of a small circle a. Find its distance from the center.

Ex. 1265. The volume of a sphere is V. Find the surface of an equilateral spherical triangle whose angle is equal to 100°.