The inner and outer diameter of a cylindrical lead pipe is 2 1 3 decimetre and 2 1 6 decimetre. By melting 7 . 2 metre pipe how many spherical balls of 6 cm diameter can be formed?

Given; Inner diameter of pipe d 1 = 2 1 3 = 7 3 decimeter ∴ Inner radius r 1 = 7 6 decimeter Outer diameter of pipe d 2 = 2 1 6 = 13 6 decimeter ∴ Inner radius r 2 = 13 12 decimeter Height of the pipe h = 7 . 2 m = 72 decimeter According to question, Volume of pipe = 2 × Volume of spherical balls 2 π r 1 2 - r 2 2 h = n × 4 3 πr 3 7 6 2 - 13 12 2 × 72 = n × 2 3 × 0 . 3 3 49 36 - 169 144 × 72 = n × 2 3 × 0 . 3 3 196 - 169 144 × 72 = n × 2 3 × 0 . 3 3 13 . 5 = n × 2 3 × 0 . 3 3 n = 13 . 5 × 3 2 × 0 . 3 × 0 . 3 × 0 . 3 = 750 Hence, 750 spherical balls can be formed.

The inner and outer diameter of a cylindrical lead pipe is 2 1 3 decimetre and 2 1 6 decimetre. By melting 7 . 2 metre pipe how many spherical balls of 6 cm diameter can be formed?

Given; Inner diameter of pipe d 1 = 2 1 3 = 7 3 decimeter ∴ Inner radius r 1 = 7 6 decimeter Outer diameter of pipe d 2 = 2 1 6 = 13 6 decimeter ∴ Inner radius r 2 = 13 12 decimeter Height of the pipe h = 7 . 2 m = 72 decimeter According to question, Volume of pipe = 2 × Volume of spherical balls 2 π r 1 2 - r 2 2 h = n × 4 3 πr 3 7 6 2 - 13 12 2 × 72 = n × 2 3 × 0 . 3 3 49 36 - 169 144 × 72 = n × 2 3 × 0 . 3 3 196 - 169 144 × 72 = n × 2 3 × 0 . 3 3 13 . 5 = n × 2 3 × 0 . 3 3 n = 13 . 5 × 3 2 × 0 . 3 × 0 . 3 × 0 . 3 = 750 Hence, 750 spherical balls can be formed.

MEDIUM

10th West Bengal Board

IMPORTANT

Earn 100

The inner and outer diameter of a cylindrical lead pipe is $2 \frac{1}{3}$ decimetre and $2 \frac{1}{6}$ decimetre. By melting $7.2$ metre pipe how many spherical balls of $6 cm$ diameter can be formed?

Important Questions on Miscellaneous Exercise : Mensuration

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 64

The vertical height of a conical shape tent is

10

metre and the diameter of the base is

15

metre. If the cost of canvas per square metre is

₹ 3.50

, find the cost of the canvas to make the tent.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 65

By melting the iron shape of sphere with diameter

\frac{5}{2} c m

, a circular iron sheet of

\frac{8}{15} c m

thickness is formed. If the radius of the sheet is

\frac{k}{4} c m

, then find the value of

k

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 66

The area of the whole surface of a hollow cylindrical pipe is

264 c m^{2}

. If the thickness of the pipe is

2 c m

, external radius is

4 c m

and its length is

k c m

, then find the value of

k

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 67

The length, breadth and thickness of a lead rectangular parallelopiped are

16

decimetres,

8

decimetres and

5.5

decimetres. Find the number of balls of diameter

2

decimetres that can be made by melting the parallelopiped.

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 68

A cylindrical pot of diameter

28 c m

is partly filled with water. A piece of iron in the form of a cone of

14 c m

diameter and

15 c m

height is completely immersed in the water will not overflow. What is an increase of water level in the pot in cm?

EASY

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 69

A solid sphere of radius $1 c m$ is melted to stretch into a wire of length $100 c m$ . Find the radius of the wire in cm.

Write your answer up to two decimal places.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 70

The area of the whole surface of a solid hemisphere is

1848 c m^{2}

. By melting the hemisphere a solid right circular cone is formed. The radius of the base of the cone is the same as the radius of the hemisphere. Find the height of the cone.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 71

A right circular cylinder of length

35 f t

and radius

5 f t

. From the piece, a rectangular parallelepiped of the square base is to be formed. How many cubic feet of wood will remain? How much wood was spent from the log?

The inner and outer diameter of a cylindrical lead pipe is 213 decimetre and 216 decimetre. By melting 7.2 metre pipe how many spherical balls of 6 cm diameter can be formed?

Important Questions on Miscellaneous Exercise : Mensuration

Learn and Prepare for any exam you want !

The inner and outer diameter of a cylindrical lead pipe is $2 \frac{1}{3}$ decimetre and $2 \frac{1}{6}$ decimetre. By melting $7.2$ metre pipe how many spherical balls of $6 cm$ diameter can be formed?