# Question f93d9

Nov 27, 2017

That's a gigantic cell!! :O :D
a) $2.56 \times {10}^{27} {\text{mm}}^{3}$ volume
b) $2.56 \times {10}^{26} L$

#### Explanation:

These are just unit conversions.
$1 {m}^{3} = 1 \times {10}^{9} m {m}^{3}$
$1 M m = 1 \times {10}^{6} m$, so $1 M {m}^{3} = 1 \times {10}^{18} m$
$1 {m}^{3} = 1000 L$

$2.56 M {m}^{3} \times {10}^{18} {m}^{3} / {\text{Mm"^3 xx 10^9"mm}}^{3} / {m}^{3} =$

$2.56 \times {10}^{27} {\text{mm}}^{3}$

$2.56 M {m}^{3} \times {10}^{18} {m}^{3} / \text{Mm"^3 xx 1 xx 10^3m^3/L xx 10^5 "cells} =$

$2.56 \times {10}^{26} L$

Nov 27, 2017

(a) $2.56 \times {10}^{-} 9 m {m}^{3}$
(b) $2.56 \times {10}^{-} 10 L$

#### Explanation:

Megameter means a million(${10}^{6}$) meters, or $1000$ kilometers. It would be too large to express the size of a bacterial cell.

The following answer is under the assumption that the volume is $2.56$ cubic $\textcolor{red}{\text{micrometers}}$. If you really want the volume of a gigantic bacterial cell, see SCooke's post.

"Micro" means one-millionth(${10}^{-} 6$).
1 μm=10^-6 m
1 μm^3 =(10^-6)^3 m^3= 10^-18 m^3#

The volume of the bacterial cell is $2.56 \times {10}^{-} 18 {m}^{3}$.

(a) $1 m {m}^{3} = {\left({10}^{-} 3\right)}^{3} {m}^{3} = {10}^{-} 9 {m}^{3}$
$2.56 \cdot {10}^{-} 18 {m}^{3} = \frac{2.56 \times {10}^{-} 18}{{10}^{-} 9} m {m}^{3} = 2.56 \times {10}^{-} 9 m {m}^{3}$.

(b) The volume of ${10}^{5}$ cell is $2.56 \times {10}^{-} 18 \cdot {10}^{5} = 2.56 \times {10}^{-} 13 {m}^{3}$.
As $1$ liter is ${10}^{-} 3$ cubic meters, the volume is
$\frac{2.56 \times {10}^{-} 13}{{10}^{-} 3} L = 2.56 \times {10}^{-} 10 L$.