NCERT Solutions for Class 7 Mathematics Chapter 15 Visualising Solid Shapes

$\begin{array}{l}\text{Q.1 Identify the nets which can be used to make cubes}\\ \text{(cut out copies of the nets and try it):}\end{array}$

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

\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{.}

$\begin{array}{l}\text{Q.2}\end{array}$ $\begin{array}{l}\text{Dice are cubes with dots on each face. Opposite faces of}\\ \text{a die always have a total of seven dots on them.}\end{array}$

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

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

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\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{.}

$\begin{array}{l}\text{Q.3}\end{array}$ $\text{Can this be a net for a die? Explain your answer.}$

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\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}

$\begin{array}{l}\text{Q.4}\end{array}$

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

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

$\begin{array}{l}\text{Q.5}\end{array}$

Match the nets with appropriate solids:

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\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{.}

$\begin{array}{l}\text{Q.6}\end{array}$

$\mathrm{Use}\mathrm{isometric}\mathrm{dot}\mathrm{paper}\mathrm{and}\mathrm{make}\mathrm{an}\mathrm{isometric}\mathrm{sketch}\mathrm{for}\mathrm{each}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{shapes}:$

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$\begin{array}{l}\text{Q.7}\end{array}$

The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.

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$\begin{array}{l}\text{Q.8}\end{array}$

Three cubes each with 2 cm edge are placed side by sideto form a cuboid. Sketch an oblique or isometric sketchof this cuboid.

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$\begin{array}{l}\text{Q.9}\end{array}$

Make an oblique sketch for each one of the given isometric shapes:

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$\begin{array}{l}\text{Q.10}\end{array}$

Give i an oblique sketch and ii an isometric sketch foreach of the following:a A cuboid of dimensions 5 cm, 3 cm and 2 cm.Is your sketch unique?b A cube with an edge 4 cm long.An isometric sheet is attached at the end of the book.You could try to make on it somecubes or cuboids ofdimensions specified by your friend.

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\text{(i) oblique sketch:}

\text{(ii) Isometric sketch:}

$\begin{array}{l}\text{Q.11}\end{array}$

What cross-sections do you get when you give ai vertical cut ii horizontal cut to the following solids?a A brick b Around applec A die d A circular pipee A nice cream cone

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$\begin{array}{l}\text{(a) A brick}\\ \text{We can give a vertical cut to a brick in the following way:}\end{array}$

\begin{array}{l}\text{(b) A round apple}\\ \text{We can give a vertical cut to a roudn apple in the following way:}\end{array}

We can give a horizontal cut to a round apple in the following way:

(c) A die

We can give a vertical cut to a die in the following ways:

\text{We can give a horizontal cut to a die in the following way:} \begin{array}{l}\end{array}

\begin{array}{l}\text{(d) A circular pipe}\\ \text{We can give a vertical cut to a circular pipe in the following way:}\end{array}

\text{We can give a horizontal cut to a circular pipe in the following way:} \begin{array}{l}\end{array}

\begin{array}{l}\text{(e) An ice cream cone}\\ \text{We can give a vertical cut to an ice cream cone in the following way:}\end{array}

$\mathrm{We}\mathrm{can}\mathrm{give}\mathrm{a}\mathrm{horizontal}\mathrm{cut}\mathrm{to}\mathrm{an}\mathrm{ice}\mathrm{cream}\mathrm{cone}\mathrm{in}\mathrm{the}\mathrm{following}\mathrm{way}:$

$\begin{array}{l}\text{Q.12}\end{array}$

A bulb is kept burning just right above the following solids.Name the shape of the shadows obtained in each case.Attempt to give a rough sketch of the shadow.(You maytry to experiment first and then answer these questions).

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\begin{array}{l}\text{The shapes of the shadows of these figures will be as follows:}\\ \text{(i) A ball}\end{array}

\text{The shape of the shadow of a ball will be a circle}\text{.} \text{(ii) A cylindrical pipe}

\text{The shape of the shadow of a cylindrical pipe will be a rectangle} \text{.} \text{(iii) A book}

\text{The shape of the shadow of a book will be a rectangle}\text{.}

$\begin{array}{l}\text{Q.13}\end{array}$

$\begin{array}{l}\text{Here are the shadows of some 3-D objects, when seen}\\ \text{under the lamp of an over head projector. Identify the}\\ \text{solid}\left(\text{s}\right)\text{that match each shadow. (There may be}\\ \text{multipleanswers for these!).}\end{array}$

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\begin{array}{l}\text{The given shadows can be obtained in case of the following}\\ \text{objects}\text{.}\\ \text{(i) Compact disk (Sphere)}\\ \text{(ii) A}\text{}\text{dice (Cube)}\\ \text{(iii) Triangular pyramid (Cone)}\\ \text{(iv) Note Book (Cuboid)}\end{array}

$\begin{array}{l}\text{Q.14}\end{array}$

$\begin{array}{l}\text{Examine if the following are true statements:}\\ \left(\text{i}\right)\text{The cube can cast a shadow in the shape of a rectangle.}\\ \left(\text{ii}\right)\text{The cube can cast a shadow in the shape of a hexagon.}\end{array}$

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\begin{array}{l}\text{A cube can cast shadow only in the shape of a square}\text{.}\\ \text{Therefore, any other shapes are not possible}\text{.}\\ \text{So,}\\ \text{(i) False}\\ \text{(ii) False}\end{array}