A solid sphere of radius 6 cm is melted into a hollow cylinder uniform thickness of the external radius of the base of the cylinder is 5 cm and its height is 32 cm find the electronic thickness of the cylinder
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A solid sphere of radius 6 cm is melted into a hollow cylinder uniform thickness of the external radius of the base of the cylinder is 5 cm and its height is 32 cm find the electronic thickness of the cylinder
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Answer:
Uniform thickness of cylinder is 1 cm.
Step-by-step explanation:
Uniform thickness of cylinder is 1 cm.
Step-by-step explanation:
Given : A solid sphere of radius 6cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5cm and its height is 32cm.
To find : The uniform thickness?
Solution :
Radius of sphere R=6 cm
External radius of cylinder
Internal radius of sphere
Height of the cylinder h=32 cm
According to question,
Volume of the cylinder= Volume of the sphere
Uniform thickness of cylinder is
Therefore, Uniform thickness of cylinder is 1 cm.
Given:
Radius of sphere = 6cm
External Radius of cylinder = 5cm
Height of the cylinder = 32cm
Find:
The thickness of the cylinder.
Solution:
Let the internal Radius of the cylinder be 'r' cm.
Let the external Radius of the cylinder be 'R' cm.
We know that;
Volume of sphere = 4/3πr³
Volume of cylinder = π(R² - r²)
=> 4/3πr³ = π(R² - r²)
=> 4/3 × (6)³ = (5² - r²) (32)
=> 4/3 × 216 = 25 - r² × 32
=> 4 × 72 = 25 - r² × 32
=> 288 = 25 - r² × 32
=> 288/32 = 25 - r²
=> 9 = 25 - r²
=> r² = 25 - 9
=> r² = 16
=> r = √16
=> r = 4cm
Internal radius = 4cm
So,
The thickness of the cylinder = (R - r)
=> 5 - 4
=> 1cm
Hence, the thickness of the cylinder is 1cm.
I hope it will help you.
Regards.