What is the volume of the larger sphere if the diameters of two spheres are in the ratio of 2:3 and the sum of their volumes is 1260 cu.m?

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Answer 1 · 2015-04-02T12:47:20

It is #972# cu.m

The volume formula of spheres is:

#V=(4/3)*pi*r^3#

We have sphere #A# and sphere #B#.

#V_A = (4/3) * pi * (r_A)^3#

#V_B = (4/3) * pi * (r_B)^3#

As we know that #r_A/r_B=2/3#

#3r_A=2r_B#
#r_B=3r_A/2#

Now plug #r_B# to #V_B#

#V_B = (4/3) * pi * (3r_A/2)^3#

#V_B = (4/3) * pi * 27(r_A)^3/8#

#V_B = (9/2) * pi * (r_A)^3#

So we can now see that #V_B# is #(3/4)*(9/2)# times bigger than #V_A#

So we can simplify things now:

#V_A = k#
#V_B = (27/8)k#

Also we know #V_A + V_B = 1260#

#k+(27k)/8 = 1260#

#(8k + 27k)/8 = 1260#

#8k + 27k = 1260*8#
#35k = 10080#
#k = 288#

#k# was the volume of #A# and the total volume was #1260#. So the larger sphere's volume is #1260-288=972#