Mathematics Class 10>Chapter 10 - Mensuration>Exercise>Q 7

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A vessel is in the form of an inverted cone. Its height is $8 cm$ and the radius of its top is $5 cm$ It is filled with water up to the rim. When lead shots, each of which is a sphere of radius $0.5 cm$ are dropped into the vessel, $\frac{1}{4}$ of the water flows out. Find the number of lead shots dropped into the vessel.

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Important Questions on Mensuration

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Mathematics Class 10>Chapter 10 - Mensuration>Exercise>Q 8

A solid metallic sphere of diameter

28 cm

is melted and recast into a number of smaller cones, each of diameter

4 \frac{2}{3} cm

and height

3 cm

. Find the number of cones so formed.

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Mathematics Class 10>Chapter 10 - Mensuration>Optional Exercise>Q 1

A golf ball has diameter equal to

4.1 cm .

Its surface has

150

dimples each of radius

2 mm

. The total surface area which is exposed to the surroundings

=

_____

{cm}^{2}

(Assume that the dimples are all hemispherical)

[π = \frac{22}{7}]

.

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Mathematics Class 10>Chapter 10 - Mensuration>Optional Exercise>Q 2

A cylinder of radius

12 cm

contains water to a depth of

20 cm .

When a spherical iron ball is dropped in to the cylinder, the level of water is raised by

6.75 cm .

Find the radius of the ball.

[π = \frac{22}{7}]

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Mathematics Class 10>Chapter 10 - Mensuration>Optional Exercise>Q 3

A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is

4.2 cm

and heights of the cylindrical and conical portions are

12 cm

and

7 cm

respectively. If the volume of the solid toy is

k \frac{8}{125} {cm}^{3}

, then find the value of

k

.

[π = \frac{22}{7}]

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Mathematics Class 10>Chapter 10 - Mensuration>Optional Exercise>Q 4

Three metal cubes with edges $15 cm, 12 cm$ and $9 cm$ respectively are melted together and formed into a single cube. Find the diagonal of this cube.

If the diagonal of the cube is $18 \sqrt{k}$ cm, then find the value of k.

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Mathematics Class 10>Chapter 10 - Mensuration>Optional Exercise>Q 5

A hemispherical bowl of internal diameter

36 cm

contains a liquid. This liquid is to be filled in cylindrical bottles of radius

3 cm

and height

6 cm

How many bottles are required to empty the bowl?