Ray's New Practical Arithmetic · Arts. 256–259 · Unit 25: Mensuration
119. Pyramids, cones and spheres
Goal: Your child finds the surface and volume of pyramids and cones, and of a sphere.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 326 gives the surface rules for pyramids and cones (Art. 256) with problems, and the volume rule (Art. 257). Page 327 has the volume problems, the surface of a sphere (Art. 258) and its volume (Art. 259). Answers are printed.
The lesson, step by step
Warm-up
Ask: If you fill a cone-shaped cup with water and pour it into a cylinder-shaped cup with the same base and height, how many cones fill the cylinder? (Three.)
Pyramid and cone
Multiply the perimeter of the base by the slant height, and take half the product.
(For a cone, use the circumference of the base.) For volume:
Multiply the area of the base by the altitude, and take one-third of the product.
Sphere
Multiply the square of the diameter by 3.1416.
for the surface, and for the volume:
Multiply the cube of the diameter by one-sixth of 3.1416, or .5236.
Guided practice
Do these together:
Find the volume of a square pyramid, of which each side of the base is 5 ft. and the altitude 21 ft.
What is the surface of a sphere, of which the diameter is 1 ft.?
Independent practice and check
Your child works the remaining problems on pages 326–327, including the great pyramid problem (477 ft. high) and the earth's surface. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: a pyramid has base area 9 and height 10, volume? A cylinder with the same base and height?