Question

The volume of a cone varies jointly with the area of the base and the height. when the area of the base is


`{27x}^(2)`
and the height is

`6cm`
the volume is

`{54}cm^(2)`
therefore the area base is blank when the height is 12cm and the volume is 124cm

`{124}cm^(3)`

Answer 1

The volume of a cone varies jointly with the area of the base and the height of the cone.


`V = kAh`

where
V = volume
k = constant of proportionality
A = area of the base
h = height of the cone

The given info is for A = 27, and h = 6, then V = 54 (all using appropriate units for area, length, and volume, respectively.)

Now we can find k, the constant of proportionality.

V = kAh

54 = k * 27 * 6

k = 54/(27 * 6)

k = 1/3

The formula is


`V = (1)/(3)Ah`

Now we use the second set of info, the height and the volume, and we find the area of the base.


`V = (1)/(3)Ah`


`124 = (1)/(3) * A * 12`


`124 = 4A`


`A = 31`

Answer: the area of the base is 31 cm^2