EASY

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Write the formula to find the length of a cuboid.

Important Questions on Mensuration

MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

Diameter of a steel ball is measured using a Vernier calipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as:

S.No.	MS (cm)	VS divisions
1.	0.5	8
2.	0.5	4
3.	0.5	6

If the zero error is - 0.03 cm, then mean corrected diameter is:

HARD

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

There are two vernier calipers both of which have $1 cm$ divided into $10$ equal divisions on the main scale. The Vernier scale of one of the calipers $(C_{1})$ has $10$ equal divisions that correspond to $9$ main scale divisions. The Vernier scale of the other caliper $(C_{2})$ has $10$ equal divisions that correspond to $11$ main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in $cm$ ) by calipers $C_{1}$ and $C_{2}$ respectively, are

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MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

The pitch and the number of divisions, on the circular scale, for a given screw gauge are

0.5 mm

and

100

respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies

3

divisions below the mean line.

The readings of the main scale and the circular scale, for a thin sheet, are

5 .5 mm

and

48

respectively, the thickness of this sheet is:

MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

A screw gauge with a pitch of

0.5 mm

and a circular scale with

50

divisions is used to measure the thickness of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the

45^{t h}

division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is

0 .5 mm

and the

25^{t h}

division coincides with the main scale line?

EASY

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

A metal cube is completely submerged in a cylindrical vessel containing water. The diameter of the vessel is $30 c m,$ the level of water is raised by $1 \frac{41}{99} c m$ . The length of the edge of the cube is:

HARD

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

Consider a Vernier calipers in which each

1 cm

on the main scale is divided into

8

equal divisions and a screw gauge with

100

divisions on its circular scale. In the Vernier calipers,

5

divisions of the Vernier scale coincide with

4

divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then:

MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

The least count of the main scale of a screw gauge is

1 mm .

The minimum number of divisions on its circular scale required to measure

5 μm

diameter of a wire is:

HARD

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

A specially designed Vernier caliper has the main scale least count of

1 mm

. On the Vernier scale, there are 10 equal divisions and they match with 11 main scale divisions. Then, the least count of the Vernier caliper is:

EASY

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

If side of each cube is $3 cm$ . Then Volume of given figure is

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MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

A cube of side

12 cm

, is painted blue on all the faces and then cut into smaller cubes each of side

3 cm

. The total number of smaller cubes having none of their faces painted blue will be

MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

If the screw on a screw-gauge is given six rotations, it moves by

3 mm

on the main scale. If there are

50

divisions on the circular scale the least count of the screw gauge is:

MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

Each side of a cube is decreased by

50 % .

Calculate the ratio of the volumes of the original and changed cube.

EASY

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

The least count of the main scale of a vernier calipers is

1 mm

. Its vernier scale is divided into

10

divisions and coincide with

9

divisions of the main scale. When jaws are touching each other, the

7^{th}

division of the vernier scale coincides with a division of the main scale and the zero of vernier scale is lying right side of the zero of the main scale. When this vernier is used to measure the length of the cylinder the zero of the vernier scale between

3.1 cm

and

3.2 cm

and

4^{th}

VSD coincides with the main scale division. The length of the cylinder is (VSD is vernier scale division)

HARD

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the zero of the vernier scale lies between

5.10 cm

and

5.15 cm

of the main scale. The vernier scale has

50

divisions equivalent to

2.45 cm

. The

24^{th}

division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is,

EASY

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

A screw gauge has

50

divisions on its circular scale. The circular scale is

4

units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of

0.5 mm

is noticed on the pitch scale. The nature of zero error involved and the least count of the screw gauge, are respectively:

EASY

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

The vernier scale used for measurement has a positive zero error of $0.2 mm .$ If while taking a measurement it was noted that $0$ on the vernier scale lies between $8.5 cm$ and $8.6 cm$ . Vernier coincidence is $6,$ then the correct value of measurement is $cm .$

(least count $= 0.01 cm$ )

MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

The pitch of the screw gauge is

1 mm

and there are

100

divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies

8

divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while

72^{nd}

division on circular scale coincides with the reference line. The radius of the wire is

MEDIUM

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

If the ratio of volumes of two cubes is

27 : 64

, then the ratio of their surface area is:

HARD

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

64

buckets of water are withdrawn from a cubical water lank, full of water, then

\frac{1}{3}

of water in the tank still remains. If the length of the side of the water tank is

12

metre, then what is the capacity (in litre) of each bucket?

(1 cubic decimeter = 1 litre)

EASY

Mathematics>Geometry>Mensuration>Volume of Cube, Cuboid and Cylinder

The volume of a cube is $1000 {cm}^{3}$ . Find its side.

Write the formula to find the length of a cuboid.

Important Questions on Mensuration

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