A cone's circular base has a diameter of 8 feet. The volume of the cone is 279 cubic feet. What is the approximate height of the cone?
Given Data :
Diameter = 8 ft
Volume of Cone = 279 ft³
Formula for Cone
[tex] \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \: \green{\underline{ \green{ \overline{ \blue{\boxed{ \frak{ \pink{Volume \: of \:Cone = πr² \frac{h}{3} }}}}}}}}[/tex]
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As we know radius is diameter/2
Radius = 8/2 = 4 ft
Now, putting the values in the formula we get
[tex] \mapsto \frak{Volume = \frac{22}{7} \times {4}^{2} \times \frac{h}{3} }[/tex]
[tex]\mapsto \frak{Volume = \frac{22}{7} \times 16 \times \frac{h}{3} }[/tex]
[tex] \mapsto \frak{Volume = \frac{352}{21} h }[/tex]
Now, putting the value of volume which is 279 ft we get
[tex] \mapsto \frak{279 = \frac{352}{21}h }[/tex]
[tex] \mapsto \frak{h = 279 \times \frac{21}{352} }[/tex]
[tex]\mapsto \frak{h = 16.64 \: ft }[/tex]
After approximating we will get the value as 16.65 ft
Hence, the correct answer is the first option i.e 16.65 ft
