Question

The length, width, and height of a rectangular pyramid are multiplied by 1/2. which of the following describes the effect on the volume.

Answer 1

the volume is multiplied by 1/8 (option D)

Step-by-step 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:

`\begin{gathered} \text{Volume = }(1)/(3)((1)/(2)l\text{ }*\text{ }(1)/(2)w\text{ }*\text{ }(1)/(2)h) \\ \text{Volume = }(1)/(3)((1)/(2)*(1)/(2)*(1)/(2)* lwh) \\ \text{Volume = }(1)/(3)((1)/(8)* lwh) \end{gathered}`

comparing with the intital volume:

`\begin{gathered} New\text{ Volume = }(1)/(3)*(1)/(8)* lwh \\ New\text{ Volume = }(1)/(8)((1)/(3)* lwh) \\ \text{New volume = }(1)/(8)(initial\text{ volume)} \end{gathered}`

Hence, the volume is multiplied by 1/8 (option D)