Question

Marlon has two lava lamps. The volume of his triangular prisms lamp is 96 cm cubed. He has another lava lamp in the shape of a triangular pyramid and it has the same base and height as the first candle. What is the difference in the volumes of the two lamps?

Answer 1

Therefore the difference in volume of the two lamps = 96
`cm^(3)` - 32
`cm^(3)` = 64
`cm^(3)`

Explanation:

i) volume of first lava lamp = base
`*` height = 96
`cm^(3)`

ii) base of first lamp = base of second lamp = base

iii) height of first lamp = height of second lamp = height

iv) volume of second lamp =
`(1)/(3)`
`*` base
`*` height

therefore volume of second lamp =
`(1)/(3)`
`*` 96
`cm^(3)` = 32
`cm^(3)`

v) therefore the difference in volume of the two lamps = 96
`cm^(3)` - 32
`cm^(3)` = 64
`cm^(3)`