Question

GEOMETRY Express the volume of each solid as a monomial. a. m3n3b. m3n4c. m4n4d. m4n5

Answer 1

SOLUTION

Consider the image given below

The image above is a cuboid and the volume of a cuboid is given by the formula

$\text{Volume of cuboid= L x W x H}$

Where

$\begin{gathered} L=length=m^3n \\ W=\text{width}=mn^3 \\ H=\text{height}=n \end{gathered}$

Substituting into the formula, we have

$\text{Volume of cuboid=m}^3n\times mn^3\times n$

Simplifying the expression we have

$m^3\times m^1\times n^1\times n^3\times n^1$

Applying the rule of indices i.e when the base are the same, we add their powers

Hence.

$\begin{gathered} m^{3+1}\times n^{1+3+1} \\ m^4\times n^5 \end{gathered}$

Therefore, the monomial becomes

$m^4n^5$

Answer ; Option D