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Solve the Exercise Exercise page 101 (Chapter 10 Math 7 Connect)
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10.17. Write the names of the vertices, sides, sides, and bases of the rectangular prism in Figure 10.40 .
Solution guide:
+ 8 vertices: M, N, P, Q, M’, N’, P’, Q’.
+ 12 edges: MN, MQ, NP, PQ, M’N’, M’Q’, N’P’, P’Q’, MM’, NN’, PP’, QQ’.
+ 4 sides: MNN’M’, NPP’N’, PQQ’P’, MQQ’M’.
+ 2 bottom faces: MNPQ, M’NP’Q’.
10.18. A cake has the shape of a triangular prism, the size is as shown in figure 10.41
a) Calculate the volume of the cake.
b) If a box has to be made to fit this cake, what is the area of material needed (regardless of the gluing edge).
Solution guide:
a) The volume of the cake is the volume of a prism whose base is a right triangle with sides equal to 6 cm and 8 cm.
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The volume of the prism is:
$\frac{1}{2}$. 6. 8. 3= 72 (cm3)
b) The area of material to be used is the area around the prism and the area of the two bases.
Using the Pythagorean theorem, the remaining side of the triangle at the base is: $\sqrt{6^{2}+8^{2}}=10$.
The amount of material needed is:
3. (6 + 8 + 10) + $\frac{1}{2}$. 6. 8 = 96 (cm2).
10.19. People dig a ditch in the shape of a prism standing quadrilateral as shown in Figure 10.42. The ditch is 20 m long, 1.5 m deep, 1.8 m wide on the surface and 1.2 m wide at the bottom. Calculate the volume of soil to be excavated
Solution guide:
The volume of soil to be excavated is the volume of the rectangular prism ABCD. A’B’C’D’
The area of the base ABCD is:
$\frac{1}{2}$.1.5. (1.8 + 1.2) = 2.25 (m2)
Volume of a vertical prism of quadrilateral ABCD. A’B’C’D’ is :
2.25. 20 = 45 (m3).
