To answer this question we will use the following formulas to compute the volume of a rectangular prism and a pyramid:
[tex]\begin{gathered} V_{prism}=Area_{base}\times height, \\ V_{pyramid}=\frac{1}{3}Area_{base}\times height. \end{gathered}[/tex]
Notice that the dollhouse is formed by a pyramid and a rectangular prism with the same base.
From the given diagram we get that the base of the rectangular prism and the pyramid is a rectangle with a length of 2.5ft and a width of 3ft, then:
[tex]Area_{base}=2.5ft\times3ft=7.5ft^2.[/tex]
From the given diagram we get that the height of the rectangular prism is 2ft, therefore:
[tex]V_{prism}=7.5ft^2\times2ft=15ft^3.[/tex]
From the given diagram we get that the height of the pyramid is 1.5ft, therefore:
[tex]V_{pyramid}=\frac{1}{3}\times7.5ft^2\times1.5ft=3.75ft^3.[/tex]
Therefore the volume of the dollhouse is:
[tex]V_{dollhouse}=V_{prism}+V_{pyramid}=15ft^3+3.75ft^3=18.75ft^3.[/tex]
Answer:
[tex]18.75ft^3.[/tex]
