## College Algebra (6th Edition)

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)
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)