Question

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Solution

Let r cm be the radius of the sphere. Then, r = 4.2 cm

Now,
Volume = $4 over 3 space πr cubed$

$equals open square brackets 4 over 3 space straight x space straight pi space straight x left parenthesis 4.2 right parenthesis space straight x space left parenthesis 4.2 right parenthesis space left parenthesis 4.2 right parenthesis close square brackets space cm cubed$

Let R cm be the radius and h cm be the height at the cylinder. Then
R = 6 cm and h = ?
Now, Volume = πR²h
= (π x 6 x 6 x h) cm³∵ Since sphere is recast into the shape of a cylinder. So, volume remains same
$bold italic i bold. bold italic e bold. bold space bold space bold space bold 4 over bold 3 bold space bold πr to the power of bold 3 bold space bold equals bold space bold πR to the power of bold 2 bold h$
$rightwards double arrow space 4 over 3 straight pi space straight x space 4.2 space straight x space 4.2 space straight x space 4.2 space equals space straight pi space straight x space 6 space straight x space 6 space straight x space straight h space space space space space space space space space space space space space space straight h space equals space fraction numerator 4 space straight x space 4.2 space straight x space 4.2 space straight x space 4.2 over denominator 6 space straight x space 6 space straight x space 3 end fraction space space space space space space space space space space space space space space space space equals space fraction numerator 296.352 over denominator 108 end fraction equals space 2.74 space cm$

For Daily Free Study Material Join wiredfaculty

Statistics

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Some More Questions From Statistics Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location