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 $1260-288=972$