How many cylinders of radius 3 cm and height 6 cm can be formed by melting sphere whose radius is 9 cm
Answers
Answer:
- Number of cylinders formed on melting the sphere = 18
Explanation:
Given,
- Radius of cylinder to be formed, r = 3 cm
- Height of cylinder formed, h = 6 cm
- Radius of sphere melted, R = 9 cm
To find,
- Number of cylinders formed on melting the sphere, x =?
Formula required,
- Formula for volume of cylinder
V of cylinder = π r² h
[ where r is radius and h is height of cylinder ]
- Formula for volume of sphere
V of sphere = 4/3 π R³
[ where R is radius of sphere ]
Solution,
Let, x cylinders are formed on melting the sphere
then,
→ V of melted sphere = x · ( V of cylinder formed )
→ 4/3 π R³ = x · ( π r² h )
→ 4/3 R³ = x · r² h
→ 4/3 · ( 9 )³ = x ( 3 )² · ( 6 )
→ 4/3 · 729 = 54 x
→ 972 = 54 x
→ x = 972 / 54
→ x = 18
Therefore,
- A total of 18 cylinders would be formed on melting the sphere.
Answer:
:
Given : -
- Cylinders of radius = 3 cm
- cylinder of Height = 6 cm
- Radius of sphere = 9 cm
To find : -
- How many cylinders
Solution : -
Let cylinders of sphere x
❂ Applying furmulas we have :
- Valume of cylinder = π r² h
- V of sphere = 4/3 π R³
Volume of melted sphere = x ×>( V of cylinder formed )
➻ 4/3 π R³ = x × ( π r² h )
putting all values :
➻ 4/3 × ( 9 )³ = x × ( 3 )² × ( 6 )
➻ 4/3 × 729 = x × 9 × 6
➻ 4/3 × 729 = 54x
➻ 4 × 243 = 54x
➻ x = 4 × 243 / 54
➻ x = 4 × 81 / 18
➻ x = 4 × 9/2
➻x = 2 × 9
➻x = 18
Hence the number of cylinders is 18
More information : -
Radius
- Radius is a line from the center to the outside of a circle or sphere.
- The definition of a radius is a circular limit or a boundary of a specific distance which is drawn from a specific point.
sphere
- a country or area in which another country has power to affect developments though it has no formal authority.