A metallic sphere of radius 6 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Share
A metallic sphere of radius 6 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Given :
To find :
Step-by-step explanation :
Since sphere is melted into a cylinder.
So, Volume os sphere = Volume of cylinder
Volume of sphere,
Radius, r = 6 cm
We know that,
Volume of sphere = 4/3 π r³
Substituting the values in the above formula, we get,
= 4/3π(6) ³
Volume of cylinder,
Radius, r = 6 cm
Let, height = h cm.
We know that,
Volume of cylinder = πr²h
Substituting the values in the above formula, we get,
= π (6)² h
= 36πh
Now,
Volume of sphere = Volume of cylinder
Substituting the values, we get,
4/3π(6)³ = 36πh
4/3π(6)³× 1/3π = h
h = 4/3π(6)³ × 1/36π
h = 4/3(6)³ × 1/36
h = 4/3 × 6 × 6 × 6 × 1/36
h = 6 × 6 × 6/27
h = 6 × 6 × 6/3 × 3 × 3
h = 2 × 2 × 2
h = 8.
Therefore, Height of cylinder = 8 cm.
Verified answer
Answer:
V(sp) = V(cyl)
4/3*pi*r,³ = pi*r²*h
4/3 * 6³ = 6²*h
=> 4/3 * 6 = h
=> h = 8 cm