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Practice each question, then open the answer or worked solution.
Out of the following which is a ${\mathbf{3}}$-D figure?
(a) Square
(b) Sphere
(c) Triangle
(d) Circle
Ans: Option (b) is the correct answer.
The ${\text{3 - D}}$ figure is defined as the figure which has three dimensions, that is, length, width and height. Square, Triangle and Circle have only two dimensions. So, they are two dimensional figures. Therefore, option (b) is the correct answer.
Total number of edges a cylinder has
(a) ${\mathbf{0}}$
(b) ${\mathbf{1}}$
(c) ${\mathbf{2}}$
(d) ${\mathbf{3}}$
Ans: Option (c) is the correct answer.
A cylinder has 2 edges, 3 faces and 0 vertices.
A solid that has two opposite identical faces and other faces as parallelograms is a
(a) prism
(b) pyramid
(c) cone
(d) sphere
Ans: Option (a) is the correct answer.
A solid that has two opposite identical faces and other faces as parallelograms is a Prism.
Therefore, option (a) is the correct answer.
The solid with one circular face, one curved surface and one vertex is known as:
(a) cone
(b) sphere
(c) cylinder
(d) prism
Ans: Option (a) is the correct answer.
The solid with one circular face, one curved surface and one vertex is known as Cone.
Therefore, option (a) is the correct answer.
If three cubes each of edge ${\mathbf{4cm}}$ are placed end to end, then the dimensions of resulting solid are:
(a) ${\mathbf{12cm \times 4cm \times 4cm}}$
(b) ${\mathbf{4cm \times 8cm \times 4cm}}$
(c) ${\mathbf{4cm \times 8cm \times 12cm}}$
(d) ${\mathbf{4cm \times 6cm \times 8cm}}$
Ans: Option (a) is the correct answer.
If three cubes each of edge ${\mathbf{4cm}}$ are placed end to end, then the dimensions of the resulting solid are ${12cm \times 4cm \times 4cm}$. Therefore, option (a) is the correct answer.
When we cut a corner of a cube as shown in the figure 12.19, we get the cutout piece as:
(a) square pyramid
(b) trapezium prism
(c) triangular pyramid
(d) a triangle
Ans: Option (c) is the correct answer.
When we cut a corner of a cube as shown in the figure, we get the cutout piece as a triangular pyramid. Therefore, option (c) is the correct answer.
If we rotate a right-angled triangle of height ${\mathbf{5cm}}$ and base ${\mathbf{3cm}}$ about its height a full turn, we get
(a) cone of height ${\mathbf{5cm}}$, base ${\mathbf{3cm}}$
(b) triangle of height ${\mathbf{5cm}}$, base ${\mathbf{3cm}}$
(c) cone of height ${\mathbf{5cm}}$, base ${\mathbf{6cm}}$
(d) triangle of height ${\mathbf{5cm}}$, base ${\mathbf{6cm}}$
Ans: Option (a) is the correct answer.
So, if we rotate a right-angled triangle of height ${\text{5cm}}$ and base ${\text{3cm}}$ about its height a full turn, we get cone of height ${\text{5cm}}$, base ${\text{3cm}}$. Therefore, option (a) is the correct answer.
If we rotate a right-angled triangle of height $5{\text{cm}}$ and base $3{\text{cm}}$ about its base, we get:
(a) cone of height ${\mathbf{3cm}}$ and base ${\mathbf{3cm}}$
(b) cone of height ${\mathbf{5cm}}$ and base ${\mathbf{5cm}}$
(c) cone of height ${\mathbf{5cm}}$ and base ${\mathbf{3cm}}$
(d) cone of height ${\mathbf{3cm}}$ and base ${\mathbf{5cm}}$
Ans: Option (d) is the correct answer.
So, if we rotate a right-angled triangle of height $5{\text{cm}}$ and base $3{\text{cm}}$ about its base, we get cone of height $3{\text{cm}}$ and base $5{\text{cm}}$. Therefore, option (d) is the correct answer.
When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of
(a) square
(b) rectangle but not a square
(c) circle
(d) triangle
Ans: Option (b) is the correct answer.
The cube can cast a shadow in the form of a rectangle. So, when a torch is pointed towards one of the vertical edges of a cube, you get a shadow of the cube in the shape of a rectangle. Therefore, option (b) is the correct answer.
Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle:
(a) ${\mathbf{3cm,4cm,6cm}}$
(b) ${\mathbf{9cm,16cm,26cm}}$
(c) ${\mathbf{1}}{\mathbf{.5cm,3}}{\mathbf{.6cm,3}}{\mathbf{.9cm}}$
(d) ${\mathbf{7cm,24cm,26cm}}$
Ans: Option (c) is the correct answer.
From the Pythagoras theorem,
Hypotenuse $^2 = $ base $^2 + $ height $^2$
Consider $3.9{\text{cm}}$ is the length of the hypotenuse.
Then, ${(3.9)^2} = {(1.5)^2} + {(3.6)^2}$
$15.21 = 2.25 + 12.96$
Add the numbers,
$15.21 = 15.21$
For option (a),
From the Pythagoras theorem,
Hypotenuse $^2 = $ base $^2 + $ height $^2$
Consider $6{\text{cm}}$ is the length of the hypotenuse.
Then, ${(6)^2} = {(4)^2} + {(3)^2}$
$36 = 16 + 9$
$36 \ne 25$
For option (b),
From the Pythagoras theorem,
Hypotenuse $^2 = $ base $^2 + $ height $^2$
Consider $26{\text{cm}}$ is the length of the hypotenuse.
Then,${(26)^2} = {(16)^2} + {(9)^2}$
$676 = 256 + 81$
$676 \ne 337$
For option (d),
From the Pythagoras theorem,
Hypotenuse $^2 = $ base $^2 + $ height $^2$
Consider $26{\text{cm}}$ is the length of the hypotenuse.
Then,${(26)^2} = {(24)^2} + {(7)^2}$
$676 = 576 + 49$
$676 \ne 625$
Therefore, option (c) is the correct answer.