NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes (EX 15.1) Exercise 15.1

Q.1

$\begin{array}{l}\text{Identify the nets which can be used to make cubes}\\ \text{(cut out copies of the nets and try it):}\end{array}$

Ans

$\left(i\right)\mathrm{The}\mathrm{given}\mathrm{net}\mathrm{can}\mathrm{be}\mathrm{folded}\mathrm{as}:$

\begin{array}{l}\text{When the faces that are in sky blue colur and in pink colour}\\ \text{are folded to make cube, they will be overlaping each other}\text{.}\end{array}

\text{(ii) The given net can be folded as:}

\text{Thus, a cube can thus be formed in above way}\text{.}

\text{(iii) The given net can be folded as:}

\text{Thus, a cube can thus be formed in above way}\text{.}

\text{(iv) The given net can be folded as:}

\text{Thus, a cube can thus be formed in above way}\text{.}

\text{(v) The given net can be folded as:} \begin{array}{l}\end{array}

\begin{array}{l}\text{When the faces are in blue colour and in red colour are folded}\\ \text{to make a cube, they will be overlapping each other}\text{.}\end{array}

\begin{array}{l}\text{(vi) The given net can be folded as:}\end{array}

\text{Thus, a cube can thus be formed in above way}\text{.}

Q.2

$\begin{array}{l}\text{Dice are cubes with dots on each face. Opposite faces of}\\ \text{a die always have a total of seven dots on them.}\end{array}$

$\begin{array}{l}\text{Here are two nets to make dice}\left(\text{cubes}\right)\text{; the numbers}\\ \text{inserted in each square indicate the number of dots in}\\ \text{that box.}\end{array}$

$\begin{array}{l}\text{Insert suitable numbers in the blanks, remembering that}\\ \text{the number on the opposite faces should total to 7.}\end{array}$

Ans

\begin{array}{l}\text{(i) The numbers can be inserted as follows so as to make the}\\ \text{given net into a net of a dice}\text{.}\end{array}

\begin{array}{l}\text{It can be seen that the sum of opposite faces is 7}\text{.}\\ \\ \text{(ii) The numbers can be inserted as follows so as to make the}\\ \text{given net into a net of a dice}\text{.}\end{array}

\text{It can be seen that the sum of opposite faces is 7}\text{.}

Q.3

$\text{Can this be a net for a die? Explain your answer.}$

Ans

\text{The given net can be folded as:}

\begin{array}{l}\text{It can be observed that the opposite face of the dice so formed}\\ \text{have 2 and 5, 1 and 4, 3 and 6 on them}\text{.}\\ \text{The sum of numbers on the opposite faces comes to 7, 5 and 9}\\ \text{respectively}\text{.}\\ \text{However, in case of a dice, the sum of numbers on the opposite}\\ \text{faces should be7}\text{.}\\ \text{Therefore, this net is not of a dice}\text{.}\end{array}

Q.4

$\begin{array}{l}\text{Here is an incomplete net for making a cube. Complete}\\ \text{it in at least two different ways. Remember that a cube}\\ \text{has six faces. How many are there in the net here?}\\ \text{(Give two separate diagrams. If you like, you may use a}\\ \text{squared sheet for easy manipulation.)}\end{array}$

Ans

\text{There are 3 faces given in the net}\text{. The given net can be completed as:}

Q.5

$\mathrm{Match}\mathrm{the}\mathrm{nets}\mathrm{with}\mathrm{appropriate}\mathrm{solids}:$

Ans

\text{Consider net (i) It can be folded as:}

\text{Consider net (ii) It can be folded as:}

\text{It is a net of cube}\text{. Hence, (a) is the correct option}\text{.}

\text{Consider net (iii) It can be folded as:}

\text{It is a net of cylinder}\text{. Hence, (b) is the correct option}\text{.}

\text{Consider net (iv) It can be folded as:}

\text{It is a net of cone}\text{. Hence, (c) is the correct option}\text{.}