Ray's New Practical Arithmetic · Arts. 253–255 · Unit 25: Mensuration
118. Solids: surface and volume of prisms and cylinders
Goal: Your child names the common solids and finds the surface and the volume of prisms and cylinders.
You'll need
- Paper and pencil, or a slate or small whiteboard
- A box, a can with a paper label, and a ball
What's in the book
Pages 323–324 give the definitions of solids (Art. 253). Pages 324–325 give the rules for surfaces (Art. 254) with problems. Page 325 gives the volume rule (Art. 255), and page 326 its last problem. Answers are printed.
The lesson, step by step
Warm-up
Gather a box, a can and a ball. Ask your child to describe how each is different.
The words
A solid, or body, has length, breadth, and thickness.
A prism is a solid with two parallel bases, which are polygons, and with its faces parallelograms.
A cylinder is a solid with two parallel bases, which are circles, and with a curved surface.
The volume of a body is its solid contents.
Surface
Multiply the perimeter of the base by the altitude.
That gives the sides of a right prism (for a cylinder, use the circumference instead). For the whole surface:
To the convex surface add the areas of the two bases.
Unroll a paper label from a can to see why the curved part is a rectangle.
Volume
Multiply the area of the base by the altitude.
Find the volume of a cylinder whose altitude is 12 ft. and the radius of the base 2 ft.
The base is 2 × 2 × 3.1416 = 12.5664 sq. ft.; × 12 = 150.8 cu. ft., nearly.
Guided practice
Do these together:
Find the surface of a cube, each side being 37 in.
How many cubic yards in a room 24 ft. long, 18 ft. 6 in. wide, and 10 ft. 7 in. high?
Independent practice and check
Your child works the remaining surface and volume problems on pages 325–326. 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.