...similar right triangles about homologous sides. 959. COR. III. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii...

...respective altitudes and r, r' the respective radii. Can you show that the volumes of these cones are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases, or as the cubes of the diameters of their bases? Sug. Let V = volume of (I) and v = volume of (2)....

...i^' Therefore 966. COR. I 967, COR. II. The volumes of two similar cones of revolution are to eacli other as the cubes of their altitudes, or as the cubes of the radii of their bases. Hint. — The method of proof is the same as that followed in § 942. 068. Def. — The altitude of...

...themselves are to each other as the cubes of their homologous edges. 432. COR. 2. Similar prisms are to each other as the cubes of their altitudes, or as the cubes of any other homologous lines. 433. COR. 3. Since the cylinder is the limit of a prism of infinite number...

...proposition. Can you make an arithmetical formula for this proposition ? EXERCISES. 498. The lateral areas of two similar cones of revolution are to each other as the squares of their slant height, or the squares of their altitudes, or the squares of the radii of their...

...squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. Given S and s the lateral areas, T and t the total areas, V and v the volumes, H and h the altitudes,...

...squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. Given S and s the lateral areas, T and t the total areas, V and v the volumes, H and h the altitudes,...

...of the cubes of their radii? SOLID GEOMETRY. — BOOK IX. Theorem. The volumes of simitar cylinders of revolution are to each other as the cubes of their altitudes, or as the cubes of their radii. Data : Any two similar cylinders of revolution, whose altitudes are H and H', and radii...

...other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T' the total areas, V, V the volumes, H, H' the...

...of the base, B = -irR2. § 463 PROPOSITION XLI. THEOREM. 726. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their radii, or as the squares of their slant heights...