An ice cream ball of diameter $6cm.$ is placed over a cone of radius $2.5cm.$ and height $10cm.$ . Is the cone big enough to hold all the ice cream if it melts?

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Answer 1 · 2017-04-28T16:55:27

No.

To find the area of the first sphere, us the formula $A=4*pi*r^2$
$A=4*pi*3^2$
$A=113.1cm^2$
That is the area of the "ice cream scoop."

To find the area of the cone use the formula
$A=πrl+πr2$ ............( $l=sqrt(r^2+h^2)$ )
$A=100.6cm^3$
That is the area of the "cone."

Scoop Area: $113.1cm^3$
Cone Area: $100.6cm^3$

Answer 2 · 2017-04-28T17:05:32

The cone is not big enough to hold all the ice cream if it melts.

As volume of a sphere with radius $r$ is $4/3pir^3$ ,

and diameter of sphere is $6$ $cm.$ (i.e. radius $3$ $cm.$ )

its volume is $4/3pixx3^3=36pi$

Volume of a cone of radius $r$ and height is $h$ is $1/3pir^2h$ .

Diameter of cone is $5$ $cm.$ i.e. radius is $2.5$ $cm.$ and its height is $10$ $cm.$ ,

its volume is $1/3pixx2.5^2xx10=62.5/3pi=20.8333pi$

As it is less then $36pi$ , the volume of scoop of ice-cream,

the cone is not big enough to hold all the ice cream if it melts.

An ice cream ball of diameter 6cm.6cm. is placed over a cone of radius 2.5cm.2.5cm. and height 10cm.10cm.. Is the cone big enough to hold all the ice cream if it melts?