Question

A cone is 8.4 cm high and the radius of its base is 2.1 cm. it is melted and recast into a sphere. Find the radius of the sphere.

Solution

Let r cm be the radius and h cm be the height of a cylinder, then
r = 2.1. cm, h = 8.4 cm
Let r₁ cm be the radius of a sphere.
Since a sphere is made out of a cone, so their volumes are equal.
Therefore,
$rightwards double arrow space space space space space space space 1 third πr squared straight h space space space equals space 4 over 3 πr subscript 1 cubed rightwards double arrow space space space space space space space space straight r squared straight h space equals space 4 straight r subscript 1 cubed rightwards double arrow space space space 2.1 space straight x space 2.1 space straight x space 8.4 space equals space 4 space straight x space straight r subscript 1 cubed rightwards double arrow space space space straight r subscript 1 cubed space equals space fraction numerator 2.1 space straight x space 2.1 space straight x space 8.4 over denominator 4 end fraction rightwards double arrow space space straight r subscript 1 cubed equals space 2.1 space straight x space 2.1 space straight x space 2.1 rightwards double arrow space space straight r subscript 1 space equals space 2.1 space cm$

For Daily Free Study Material Join wiredfaculty

Statistics

A cone is 8.4 cm high and the radius of its base is 2.1 cm. it is melted and recast into a sphere. Find the radius of the sphere.

Some More Questions From Statistics Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location