The area of a circle is found by multiplying the circumference by one half the radius. 2d Method. Examine the circle inscribed in the square. Observe : 1. That the diameter of the circle is just equal to the side of the square. 2. That much of the surface of the square, but not all of it lies within the circumference. Careful measurement shows that about .7854 of the area of any square lies within the circumference of the inscribed circle. The area of a circle is found by multiplying the area of the square on its diameter by .7854. 19. A circle 20 ft. in diameter is inscribed in a square. What is the area of one of the corners within the square, but outside the limits of the circle? 20. A circular fountain 20 ft. in diameter is surrounded by a cement walk 4 ft. wide. How much will the walk cost at $1.50 per square yard? NOTE. - Find the difference between the areas of the two circles, the first bounded by the circumference of the fountain, and the second, by the circumference of the walk, may be placed on 1 square foot of surface. 4. How many cubes would make 12 such layers? 5. Show that 1728 cubic inches equal 1 cubic foot. 6. How many 1-inch cubes can be put into a cubical box whose edge is 3 inches? 7. How many 1-foot cubes can be placed on 9 square feet of surface? (Make diagram.) 8. How many cubes are there in three such layers? 9. Show that 27 cubic feet equal 1 cubic yard. Learn this table of solid or cubic measure: = 1 cubic yard (cu. yd.) 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) = 1 cord of wood or tanbark = = 1 cord of stone = 1 cubic yard of earth equals 1 load. The unit of cubic measure is a cube whose edge is one of the linear units; thus, a cube each edge of which is one inch in length is a cubic inch. A cubic foot is a cube whose edge is one foot. A cubic yard is a cube whose edge is one yard. A cord of wood or tanbark is a pile of 4-foot wood or tanbark 8 feet long and 4 feet high. A cord of short wood is a pile of short lengths 8 feet long and 4 feet high. The number of cords of short wood in a pile is found by dividing the number of square feet in one side by 32. Surface of Rectangular Solids How is the surface of each face found? How many faces has this solid? Show that the sum of the faces in this solid is the surface of the solid. A rectangular solid is a solid bounded by six rectangular surfaces. SOLIDS 1. How many faces has this solid? What is their shape? compare in size? How do they A cube is a solid bounded by six equal square faces. 2. Every 1-inch cube rests on how many square inches of surface? 3. Show that 144 one-inch cubes may be placed on 1 square foot of surface. 4. How many cubes would make 12 such layers? 5. Show that 1728 cubic inches equal 1 cubic foot. 6. How many 1-inch cubes can be put into a cubical box whose edge is 3 inches? 7. How many 1-foot cubes can be placed on 9 square feet of surface? (Make diagram.) 8. How many cubes are there in three such layers? 9. Show that 27 cubic feet equal 1 cubic yard. Learn this table of solid or cubic measure: = =1 cubic yard (cu. yd.) 1728 cubic inches (cu. in.) 1 cubic foot (cu. ft.) = 1 cord of wood or tanbark 1 cubic yard of earth equals 1 load. The unit of cubic measure is a cube whose edge is one of the linear units; thus, a cube each edge of which is one inch in length is a cubic inch. A cubic foot is a cube whose edge is one foot. A cubic yard is a cube whose edge is one yard. A cord of wood or tanbark is a pile of 4-foot wood or tanbark 8 feet long and 4 feet high. A cord of short wood is a pile of short lengths 8 feet long and 4 feet high. The number of cords of short wood in a pile is found by dividing the number of square feet in one side by 32. Surface of Rectangular Solids How is the surface of each face found? How many faces has this solid? Show that the sum of the faces in this solid is the surface of the solid. A rectangular solid is a solid bounded by six rectangular surfaces. |