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Maths-

General

Easy

Question

A Hollow sphere of internal and external diameters of 6 cm and 10 cm respectively is melted into a cone of 8 cm base diameter . Find the height of the cone ?

hint Hint:

Volume of the cone is $equals 1 third pi r squared h$
Volume of hollow sphere $4 over 3 pi r cubed$

The correct answer is: 24.499cm

Explanation:

We have given a Hollow sphere of internal and external diameters of 6 cm and 10 cm respectively is melted into a cone of 8 cm base diameter.

We have to find the height of the cone.

Step 1 of 1:
We have given a hollow sphere with internal and external diameter 6cm, 8cm, repectivley.
The inner and outer radius if the sphere will be 3cm, 4cm
So,
The volume of the hollow sphere will be
$V equals 4 over 3 pi open parentheses r subscript o superscript 3 minus r subscript i superscript 3 close parentheses$
$equals 4 over 3 pi open parentheses 5 cubed minus 3 cubed close parentheses$
$equals 4 over 3 pi cross times 98$
$equals 410.50 cm cubed$
Now the sphere is melted into cone with diameter $8 cm not stretchy rightwards double arrow r equals 4 cm$
So, The volume of the material of sphere = volume of the cone
So,
V = 410.50
$not stretchy rightwards double arrow 1 third pi left parenthesis 4 right parenthesis squared h equals 410.50$
$rightwards double arrow$ h = 24.499cm

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