7th Grade > Mathematics
VISUALISING SOLID SHAPES MCQs
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We need a square with same side length as that of the triangle. The resultant solid is known as a square pyramid.
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Answer: 1 Mark each
The key feature of a sphere is that every point on the surface of a sphere is equidistant from the centre.
The normal definition of faces, vertices and edges are not appropriate for a sphere because it is not a polyhedron.
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Explanation: 2 Marks
A square prism has a square as its base. However, its height is not necessarily same as the side of the square.
Thus, a square prism can also be a cuboid.
All cubes are square prism but all square prisms need not be cubes.
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Definition: 2 Marks
Example: 1 Mark
A shape that has only two dimensions (such as width and height) and no thickness is known as 2-D shape. In 2-D shapes, the sides are made of straight and curved lines.
Example: squares, circles, triangles
A 3-D shape is a solid which encloses volume and has length, breadth and height. 3-D shapes have four properties that set them apart from 2-D shapes: faces, vertices, edges and volume.
Example: sphere, cylinder, cube
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Explanation: 1 Mark each
A cylinder can be thought of as a circular prism that is a prism with a circle as its base.
A cone can be thought of a circular pyramid that is a pyramid with a circle as its base.
There are 18 boxes on a shelf.
(a) How many boxes in total can be kept on the shelf without leaving any space?
(b) If the length and height of the shelf are doubled, how many boxes can be kept on the shelf now without leaving any space?
(c) If the length is halved and height of the shelf is doubled, how many boxes can be kept on the shelf now without leaving any space?
(d) If the length is doubled and height of the shelf is halved, how many boxes can be kept on the shelf now without leaving any space?
[4 MARKS]
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Each part: 1 Mark
From visual estimation, each column contains 4 boxes.
(a) 6 columns can be fit in the shelf.
In the 5th column, there is space for 2 more boxes.
and in the 6th column, there is space for 4 boxes.
∴ Number of boxes on the full shelf = 18 + 2 + 4 = 24 boxes
(b) If the length of the shelf is doubled, the shelf can have 12 columns.
If the height of the shelf is doubled, then each column can have 8 boxes.
∴ Total number of boxes on the full new shelf:
= 12×8
= 96 boxes
(c) If the length of the shelf is halved, the shelf can have 3 columns.
If the height of the shelf is doubled, then each column can have 8 boxes
∴ Total number of boxes on the full new shelf:
= 3×8
= 24 boxes
(d) If the length of the shelf is doubled, the shelf can have 12 columns.
If the height of the shelf is doubled, then each column can have 4 boxes.
∴ Total number of boxes on the full new shelf:
= 12×4
= 48 boxes
(a) If two cubes of dimensions 3 cm by 3 cm by 3 cm are placed side by side, then what is the resulting dimension(length (l), breadth (b) and height (h)) of the cuboid? Find the value of l+b+h (in cm).
(b) A metallic cylinder with volume 1331 cm3 is melted and is transformed into a cube. What will be the length of the sides of the cube formed? (Volume of a cube with side length a is given as a3)
[3 MARKS]
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Each Part: 1.5 Marks
(a) When we put the cubes side by side, the lengths of both the cubes are added, but there will be no change in the breadth and height of the cube.
Length (l) = (3 + 3) = 6 cm.
Breadth (b) = 3 cm.
Height (h) = 3 cm.
Hence, l+b+h=6+3+3=12cm
(b) Since the metallic cylinder is melted to form a cube, the cube will be of the same volume as that of the cylinder.
Volume of cube = Volume of cylinder
a3=1331cm3
a=3√(1331)=11 cm