90.3k views
3 votes
The length, width, and height of a right rectangular prism are multiplied by 23. What will be the effect on the volume of the prism?

The volume is multiplied by 2/3.
The volume is multiplied by 8/27.
The volume is multiplied by 4/9.
The volume is multiplied by 3/2.

User Timathon
by
7.6k points

1 Answer

2 votes

Since none of the options make sense with 23, I assume it was a typo, and you meant 2/3.

Let l,w and h be the length, width and height of the original prism, and l',w' and h' be the length, width and height of the new prism. We are given


l' = l* \cfrac{2}{3},\quad w' = w* \cfrac{2}{3},\quad h' = h* \cfrac{2}{3}

Also, if we call V the original volume, and V' the volume of the new prism, we have


V = lhw,\quad V'=l'h'w'

Substitute the expressions for l', h' and w' in the formula for V':


V'=l'h'w' = l* \cfrac{2}{3}* w* \cfrac{2}{3}* h* \cfrac{2}{3} = l* h * w * \cfrac{2}{3}*\cfrac{2}{3}*\cfrac{2}{3} = V * \left(\cfrac{2}{3}\right)^3 = V*\cfrac{8}{27}

User Feralvam
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories