RD Sharma solution class 8 chapter 19 Visualising Shapes Exercise 19.2

Exercise 19.2

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Question 1:

Which among the following are nets for a cube?

Answer 1:

$$\begin{gathered} \text{To create a cube, we need six equal faces that enclose a closed box.} \\ \text{In the given figure, only (iv), (v) and (vi) are such nets that enclose } \\ \text{a box when we fold each face from the edge.} \end{gathered}$$

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Question 2:

Name the polyhedron that can be made by folding each net:

Answer 2:

$$\begin{gathered} \text{(i)} \\ \text{If we fold the given figure from the edges, we'll get a pyramid with a square base.} \end{gathered}$$
 

$$\begin{gathered} \text{(ii)} \\ \mathrm{If we fold the given }\mathrm{polyhedron} from the edges\text{, we'll get a triangular prism.}\frac{}{} \end{gathered}$$


$$\begin{gathered} \text{(iii)} \\ \mathrm{If we fold the given }\mathrm{polyhedron} from the edges,\text{ we'll get a triangular prism.} \end{gathered}$$



$$\begin{gathered} \text{(iv)} \\ \mathrm{If we fold the given }\mathrm{polyhedron} \mathrm{from the edges,}\text{ we'll get a hexagonal prism.} \end{gathered}$$



$$\begin{gathered} \text{(v)} \\ \mathrm{If we fold the given} \mathrm{net} \mathrm{from the edges,}\text{ we'll get a hexagonal pyramid.} \end{gathered}$$



$$\begin{gathered} \text{(vi)} \\ \mathrm{If we fold the given} \mathrm{net} \mathrm{from the edges,}\text{ we'll get a cuboid.} \end{gathered}$$

Question 3:

Dice are cubes where the numbers on the opposite faces must total 7. Which of the following are dice?

Answer 3:

$$\begin{gathered} \text{Among the given figures, only figure (i) is a dice.} \\ \text{This is because if we fold the given net from the edges, we'll get a cube in which the sum of the opposite faces is 7.} \end{gathered}$$

Question 4:

Draw nets for each of the following polyhedrons:

Answer 4:

(i)


(ii)


(iii)


(iv)

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Question 5:

Match the following figures:

Answer 5:

$$\begin{gathered} \text{(a)} \\ \text{The given figure is a cuboid with sides 4, 4 and 6 units.} \\ \text{Area of a rectangle =length×width} \\ \therefore \text{ Area of the rectangular face sith sides 4 and 4 =4×4=16} \\ \text{And, area of the other face with sides 4 and 6 =4×6=24} \\ \text{Thus, the net for the given figure will have four faces with area 24 and two faces with area 16.} \\ \text{Observe net (iv) satisfies this.} \\ \text{Thus, the net of figure (a) is net (iv).} \end{gathered}$$



$$\begin{gathered} \text{(b)} \\ \text{The given figure is a cuboid with sides 3, 3 and 8.} \\ \text{Area of a }\mathrm{rectangle}\text{ =length×width} \\ \text{∴ Area of the rectangular face sith sides 3 and 3 =3×3=9} \\ \text{And the area of the other face with sides 3 and 8 =3×8=24} \\ \text{Thus, the net for given figure will have four faces with area 24 and two faces with area 9.} \\ \text{Observe that net (i) satisfies this.} \\ \text{Thus, the net of figure (b) is net (i).} \end{gathered}$$



$$\begin{gathered} \text{(c)} \\ \text{The given figure is a cuboid with sides 3, 4 and 6.} \\ \text{Area of a }\mathrm{rectangle}\text{=length×width} \\ \therefore \mathrm{A}\text{rea of the rectangular face sith sides 3 and 4 =3×4=12,} \\ \mathrm{A}\text{rea of the rectangular face with sides 4 and 6 =4×6=24} \\ A\text{nd, area of the other face with sides 3 and 6 =3×6=18} \\ \text{Thus, the net for given figure will have two faces with area 24, two faces with area 18 and two faces with area 12.} \\ \text{Observe that net (ii) satisfies this.} \\ \text{Thus, the net of figure (c) is net (ii).} \end{gathered}$$



$$\begin{gathered} \text{(d)} \\ \text{The given figure is a cuboid with sides 3, 3 and 9.} \\ \text{Area of a }\mathrm{rectangle}\text{ =length×width} \\ \text{Area of the rectangular face with sides 3 and 3 =3×3=9,} \\ \mathrm{A}\text{nd, area of the other face with sides 3 and 9 =3×9=27} \\ \text{Thus, the net for given figure will have four faces with area 27 and two faces with area 9.} \\ \text{Observe that net (iii) satisfies this.} \\ \text{Thus, the net of figure (d) is net (iii).} \end{gathered}$$