Question

Describe how the change affects the volume of the prism or pyramid. Multiplying the height by 3/2.

Answer 1

1512 cm²

Volume is also multiplied by
`(3)/(2)`

Explanation:

The volume of a pyramid is given by the expression

`V = (1)/(3) l\cdot w\cdot h`

where l = base length, w = base width and h = height

The volume of this pyramid

`= (18\cdot 12\cdot 14)/(3) = 1008\; cm^3`

If we multiply the height by
`(3)/(2)` then new height

=
`14 \cdot (3)/(2) = 21 cm`

New Volume
`= (18\cdot 12\cdot 21)/(3) = 1512\; cm^3`

`\frac{\text{NewVolume}}{\text{Old Volume}} = (1512)/(1008) = (3)/(2)`

So volume is also multiplied by 3/2