Solve the exercise Exercises page 93 (Chapter 10 Math 7 Connect)
10.7. Name the vertices, sides, and diagonals of the cube MNPQ. EFGH in Figure 10.16
+ 8 vertices: M, Q, P, N, H, E, F, G.
+ 12 edges: MQ, MN, QP, PN, HE, EF, FG, GH, QH, ME, NF, PG.
+ 4 diagonal lines: MG, EP, QF, HN
10.8. A multi-purpose storage box has the shape of a rectangular box with a steel frame, cloth outside and dimensions as shown in Figure 10.17.
a) Calculate the volume of the box.
b) Calculate the area of fabric covering the outside surface of the box.
a) The volume of the box is:
30.40.50 = 60 000(cm3 )
b) The area of cloth covering the outside surface of the box is:
2.30.( 40 + 50) + 2.40.50 = 9400 (cm2)
10.9. An ice tray in the refrigerator has 18 cube-shaped compartments with a side of 2 cm (H.10.18). What is the total volume of all the ice cubes in the tray?
The volume of a small stone is:
23 = 8 (cm2)
The total volume of all the ice cubes in the tray is:
8.18 = 144 (cm3).
10.10. A cube of side 7 dm contains water, the depth of which is 4 dm. 25 bricks in the shape of a rectangular box with a length of 2 dm, a width of 1 dm and a height of 0.5 dm are dropped into the bin. How many decimeters does the water in the barrel rise from the top of the barrel (assuming all bricks are submerged in water and they absorb negligible water)?
The volume of the water tank is:
7.7 .7 = 343 (dm3)
Volume of water in the tank:
7.7.4 = 196 (dm3)
Volume of 25 bricks:
25. (126.96.36.199) = 25 (dm3)
Volume of water and bricks:
196 + 25 = 221 (dm3)
The water in the barrel rises from the top of the barrel is:
(343 – 221) : (7 .7) ≈ 2.49 (dm3).