ASSIGNMENT- SOLIDS OF WHICH V = 1/3 Bh
1. The lateral edge of a pyramidal church spire is 61 ft. Each side of its octagonal base is 22 ft. What will be the cost of painting the spire at 24 cents a square foot?
2. Each element of a circular conical pile of sand 6 ft. high is inclined 45° to the horizontal. How many cubic feet of sand does the pile contain?
3. The inside dimensions Of a trunk are 4 ft., 3 ft., 2 ft. Find the dimensions of a trunk similar in shape that will hold 4 times as much.
4. How many square feet of canvas are required for a conical tent 18 ft. high and 10 ft. in diameter if 10 per cent of the material is wasted?
5. A model steamboat is 2 ft. ‘3 in. long and it displaces 1.5 lb. of water. The ship of which the model is made 15 720 ft. long. What is its displacement in tons?
6. Among the interesting applications of similarity is the ease of a shadow, as here shown, where the, light is the center of similitude. If a man's profile is 12 in. in height and the similar shadow is 16 in. in height, find the ratio of the area of the profile to the area of the shadow.
7. How far from the top must you cut a conical tent in order to cut the cloth in half?
8. A well 40 ft. deep and 6.5 ft. in diameter is lined with stone 1.5 ft. thick so that the inner diameter of the well becomes
3.5 ft. Find the number of cubic feet of stone required.
9. A pyramidal roof 16 ft. in height, standing on a square base 24 ft. on a side, is covered with sheet lead ~ in. thick. (a) Find the weight of the lead if 1 cu~ in. of lead weighs 7 oz. (&) If the lead is stripped off and east into bullets, each of which is in the form of a cylinder ~ in. long and I~T in. in diameter, surmounted by a cone of the same diameter and ~ in. high, find how many bullets there will be.
10. The monument erected in Babylon by Queen Semiramis at her husband Ninus's tomb is said to have been one block of solid marble in the form of a square pyramid, the sides of whose base were 20 ft. and the height of the monument 150 ft. If the marble weighed 185 lb. per cu. ft., find the weight of the monument.
11. Find the volume of the largest pyramid which can be cut from a rectangular parallelepiped whose edges are 2 ~n. by 3 in. by 4 in. Discuss fully.
12. Find the least waste in cutting two conical blocks from a block of wood in the form of a right circular cylinder of radius 4 in. and altitude 7 in.
13. A mound of earth in the form of the solid shown in the figure has a rectangular base 17 yd. long and 8.62 yd. wide. Its perpendicular height is 5 yd., and the length on the top is 8.56 yd. Find the number of cubic yards of earth in the mound.
14. A vessel is in the form of an inverted regular square pyramid of altitude 9.87 in. and base edge 6.27 in. The depth of the water it contains is 6 in. (a) How much will the surface rise when I pt. of water is added? (One gal, 231 Cu. in.) (b) Find the wetted surface when the depth of the water is 9.23 in.
15. Find the volume of the largest cone having its circular base circumscribed about a face of a rectangular parallelepiped of dimensions 2 ft. by 3 ft. by 4 ft. and its vertex lying in the opposite face.
16. An ink bottle is in the form of a right circular cylinder with a large conical opening as shown in the figure. When it is filled level with the bottom ef the opening, it can just be turned upside down without any ink spilling. Prove that the depth of the cone is three-fifths the depth of the bottle.