Sid is packing crushed ice into a cone-shaped cThe cone has a height of 5 in. Its base has a diameter of 4 in. What is thevolume of the cone?20 320 in80 380r in 3

[tex]The\ volume\ of\ the\ cone:V=\dfrac{1}{3}\pi r^2H\\\\H=5\ in\\2r=4\ in\to r=2\ in\\\\subtitute\\\\V=\dfrac{1}{3}\pi\cdot2^2\cdot5=\dfrac{1}{3}\pi\cdot4\cdot5=\dfrac{20}{3}\pi\ (in^3)\\\\Answer:\boxed{V=\dfrac{20}{3}\pi\ in^3}[/tex]

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boffeemadrid boffeemadrid · Answer 2 · 2019-05-28T08:12:23+02:00

Answer:

(A) The volume of the cone is [tex]\frac{20}{3}{\pi}inches^3[/tex].

Step-by-step explanation:

It is given that the cone has a height of 5 inches and the base has the diameter equals to 4 inches, therefore the radius of the cone can be obtained as:

[tex]Radius=\frac{Diameter}{2}[/tex]

[tex]Radius=\frac{4}{2}=2[/tex]inches

And height=5inches

Now, the volume of the cone is obtained as:

[tex]v=\frac{1}{3}{\pi}r^2h[/tex]

Substituting the given values, we get

[tex]v=\frac{1}{3}{\pi}(2)^2(5)[/tex]

[tex]v=\frac{20}{3}{\pi}inches^3[/tex]

Thus, the volume of the cone is [tex]\frac{20}{3}{\pi}inches^3[/tex].

Hence, option A is correct.