Question

Jia designs a vase in the shape of a triangular prism. She decides

to make a smaller version of the vase. She decreases the area of
the base by 50%. She decreases the height by 50%. By what
percent does the volume of the vase change? Show your work.

Answer 1

50%

Explanation:

`volume = (area \: of \: base * \: height)/(3) \\ v = ( (1)/(2) area \: of \: base * (1)/(2) height)/(3) \\ v = ( (1)/(2) (area \: of \: base * heigh))/(3) \\ v = (1)/(2) ( (1)/(3) area \: of \: base \: * height) \\ v = (1)/(2) (v)because \: v \: = (1)/(3) area \: ofbase * height`

`(1)/(2) * 100 \\ = 50\%`