Question

jasper built a dollhouse for his younger sister. which equation shows how to determine the volume of the dollhouse? $v = 24(10)(8)+\frac{1}{3}(6)(24)(10)$ $v = 24(10)(8)+\frac{1}{2}(6)(24)(10)$ $v = 24(10)(8)+\frac{1}{2}(6)(24)(8)$ $v = 24(10)(8)+\frac{1}{3}(6)(24)(8)$

Explanation:

Step1: Volume of rectangular part

The volume of a rectangular prism is \(V = l\times w\times h\). Here, \(l = 24\), \(w = 8\), \(h = 10\). So, \(V_{rectangular}=24\times10\times8\).

Step2: Volume of triangular - prism part

The volume of a triangular prism is \(V=\text{Base Area}\times\text{length}\). The base is a triangle with height \(h = 6\) and base \(b = 24\). The area of the triangle \(A=\frac{1}{2}\times b\times h=\frac{1}{2}\times24\times6\). The length of the triangular prism (the same as the width of the rectangular part) is \(l = 8\). So, \(V_{triangular - prism}=\frac{1}{2}(6)(24)(8)\)

Answer:

\(V = 24(10)(8)+\frac{1}{2}(6)(24)(8)\)