Answer
9%
$2.81 \times 10^{-9}$ nm
Histone octamers occupy about 9% of the nuclear volume. DNA occupies about 9% of the nuclear volume. Together they occupy about 18% of the nuclear volume.
Work Step by Step
Step 1 : Volume of the histone octamers
Solution: $\pi r^{2}h = \pi \frac{9}{2}^2(5)(32\times10^{6}) =1.02\times10^{10} [nm^{3}]$
Step 2 : Find the volume of the nucleus
Solution: Diameter $6 \mu m = 6000 nm $
Radius = $3000 nm$
$\frac{4}{3} \pi r^3 = 1.13 \times10^{11} [nm^{3}]$
Step 3: What fraction of the total volume of the nucleus do the histone octamers occupy?
$\frac{1.02\times10^{10} [nm^{3}]}{1.13\times10^{11} [nm^{3}]} = 0.09
