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 27\pi27π27, pi cm^3 3 cubed of melted purple liquid. The radius of the cone is 333 cm. What is the height of the cone? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi. cm
Answers
Answer:
Bhai hamse na ho payega, apna time aayega
Answer:The height of the cone is 9 cm.
Step-by-step explanation:
This problem calls for the formula for the volume of a cone which is {V}=\pi r^2 \dfrac{h}3V=πr
2
3
h
V, equals, pi, r, squared, start fraction, h, divided by, 3, end fraction.
Hint #22 / 3
The cone has a radius of \blueD33start color #11accd, 3, end color #11accd cm and a volume of \purpleD{27\pi}27πstart color #7854ab, 27, pi, end color #7854ab cm^3
3
cubed. We can use these measurements to find the height.
\begin{aligned}\purpleD{27\pi} &= \pi \cdot\blueD3^2 \cdot \dfrac{h}{3} \\\\ \purpleD{27\pi}&= \pi \cdot 9 \cdot \dfrac{h}{3} \\\\ \purpleD{27\pi} & = 9 \pi \cdot \dfrac 13 \cdot h \\\\ \cancel{27 \pi} & = \cancel{9\pi} \cdot \dfrac 13 \cdot h \\\\ 3& = \dfrac13 \cdot h \\\\ 9 & = h\\\\ \end{aligned}
27π
27π
27π
27π
3
9
=π⋅3
2
⋅
3
h
=π⋅9⋅
3
h
=9π⋅
3
1
⋅h
=
9π
⋅
3
1
⋅h
=
3
1
⋅h
=h
Hint #33 / 3