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.