Answer:
[tex]\boxed{V = \dfrac{9b^2h}{8}}.[/tex]
Step-by-step explanation:
Let [tex]b'[/tex] denote the new side length. Since they increase by 50%, we get:
[tex]b' = b + 0.5b = 1.5b.[/tex]
The volume of a square pyramid is given by:
[tex]V = \dfrac{b'^2 h}{3}.[/tex]
Substituting [tex]b' = 1.5b[/tex], we get:
[tex]V = \dfrac{(1.5 b)^2 h}{3}=\left(\dfrac{3}{2}\right)^2\dfrac{b^2h}{2} = \dfrac{9}{4}\dfrac{b^2h}{2} = \dfrac{9b^2h}{8}.[/tex]
So the expression is:
[tex]\boxed{V = \dfrac{9b^2h}{8}}.[/tex]
