Question

Tyler built a dollhouse for his sister as shown in the diagram below. Find the volume of the dollhouse. Explain your method for finding the volume. (image attached)thank you ! :)

Answer 1

To answer this question we will use the following formulas to compute the volume of a rectangular prism and a pyramid:

`\begin{gathered} V_(prism)=Area_(base)* height, \\ V_(pyramid)=(1)/(3)Area_(base)* height. \end{gathered}`

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:

`Area_(base)=2.5ft*3ft=7.5ft^2.`

From the given diagram we get that the height of the rectangular prism is 2ft, therefore:

`V_(prism)=7.5ft^2*2ft=15ft^3.`

From the given diagram we get that the height of the pyramid is 1.5ft, therefore:

`V_(pyramid)=(1)/(3)*7.5ft^2*1.5ft=3.75ft^3.`

Therefore the volume of the dollhouse is:

`V_(dollhouse)=V_(prism)+V_(pyramid)=15ft^3+3.75ft^3=18.75ft^3.`

Answer:

`18.75ft^3.`