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Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27π27\pi27π27, pi cm3^3
3
start superscript, 3, end superscript of melted purple liquid. The radius of the cone is 3333 cm.

What is the height of the cone?
Either enter an exact answer in terms of π\piπpi or use 3.143.143.143, point, 14 for π\piπpi.

Respuesta :

Matheng
Volume of cone = [tex] \frac{1}{3} *\pi * r^{2} *h[/tex]
where: r is the radius and h is the height
given volume = 27π cm³ and radius = 3 cm.

∴ [tex] \frac{1}{3} *\pi * r^{2} *h = 27 \pi[/tex]
∴ [tex] \frac{1}{3} *\pi * 3^{2} *h = 27 \pi[/tex]
Solve to find h
∴ h = 9 cm.

∴ The height of the cone is 9 cm.

The height of the cone is 9 cm.

What is the volume of a cone?

The volume of a cone is given by the following formula;

[tex]\rm Volume =\dfrac{1}{3}\pi r^2h[/tex]

Where: r is the radius and h is the height.

The given value of volume = 27π cm³ and radius = 3 cm.

Substitute of the value in the formula

[tex]\rm Volume =\dfrac{1}{3}\pi r^2h\\\\27\pi =\dfrac{1}{3}\pi r^2h\\\\\h = \dfrac{27\pi \times 3 }{\pi \times (3)^2}\\\\h = \dfrac{27\pi \times 3 }{\pi \times 9}\\\\h =3 \times 3\\\\h=9[/tex]

Hence, the height of the cone is 9 cm.

Learn more about cone here;

https://brainly.com/question/360235

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