Answer
Formula for the Volume of the region outside smaller rectangular solid and inside larger rectangular solid = ($a^{2}$ $\times$ 3a) - ($b^{2}$ $\times$ 3a)
= ($a^{2}$ - $b^{2}$) 3a
Factor of formula =(a-b)(a+b)(3a)
Work Step by Step
Given rectangular solids are rectangular prisms
Volume of larger rectangular solid = (Area of larger rectangular solid base $\times$ height of rectangular solid)
Base of rectangular solid is a square so the area of larger rectangular base = $a^{2}$ (given that the side of square is a)
Height of rectangular solid = 3a
Volume of larger rectangular solid = $a^{2}$ $\times$ 3a
Volume of smaller rectangular solid = (Area of smaller rectangular base $\times$ height of rectangular solid)
Base of rectangular solid is a square so the area of smaller rectangular base = $b^{2}$ (given that the side of square is b)
Height of rectangular solid = 3a
Volume of larger rectangular solid = $b^{2}$ $\times$ 3a
Volume of the region outside smaller rectangular solid and inside larger rectangular solid = Volume of larger rectangular solid - Volume of smaller rectangular solid
Volume of the region outside smaller rectangular solid and inside larger rectangular solid = ($a^{2}$ $\times$ 3a) - ($b^{2}$ $\times$ 3a)
= ($a^{2}$ - $b^{2}$) $\times$ 3a
Formula for the Volume of the region outside smaller rectangular solid and inside larger rectangular solid = ($a^{2}$ - $b^{2}$) 3a
Use the formula ($a^{2}$ - $b^{2}$) =(a-b)(a+b)
Factor of formula =(a-b)(a+b)(3a)
