Mathematics: The volume of a cone varies jointly with the area of the base and the height. when the area of the base is [tex] {27x}^{2} [/tex] and the height is [tex]6cm[/tex]the volume is [tex] {54}cm^{2} [/tex]therefore the area base is blank when the height is 12cm and the volume is 124cm[tex] {124}cm^{3} [/tex]

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The volume of a cone varies jointly with the area

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surfer89

14.03.2022

Mathematics

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

$V = \dfrac{1}{3}Ah$

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

$V = \dfrac{1}{3}Ah$

$124 = \dfrac{1}{3} \times A \times 12$

124 = 4A

the area of the base is 31 cm^2

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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 ${124}cm^{3}$

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The volume of a cone varies jointly with the area of the base and the height. when the area of the base is and the height is the volume is therefore the area base is blank when the height is 12cm and the volume is 124cm

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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 ${124}cm^{3}$