the volume is multiplied by 1/8 (option D)
Explanation:
The shape is a rectangular pyramid
The volume of a rectangular pyramid = 1/3 (length × width × height) = 1/3 (lwh)
let initial length = l, initial height = h, initial width = w
New length = 1/2(initial length) = 1/2(l)
New height = 1/2 (initial height) = 1/2 (h)
New width = 1/2 (initial width) = 1/2 (w)
The new volume becomes:
[tex]\begin{gathered} \text{Volume = }\frac{1}{3}(\frac{1}{2}l\text{ }\times\text{ }\frac{1}{2}w\text{ }\times\text{ }\frac{1}{2}h) \\ \text{Volume = }\frac{1}{3}(\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times lwh) \\ \text{Volume = }\frac{1}{3}(\frac{1}{8}\times lwh) \end{gathered}[/tex]
comparing with the intital volume:
[tex]\begin{gathered} New\text{ Volume = }\frac{1}{3}\times\frac{1}{8}\times lwh \\ New\text{ Volume = }\frac{1}{8}(\frac{1}{3}\times lwh) \\ \text{New volume = }\frac{1}{8}(initial\text{ volume)} \end{gathered}[/tex]
Hence, the volume is multiplied by 1/8 (option D)
