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Find the diameter of a cone that has a volume of 83.74 cubic inches and a height of 5 inches. use 3.14 for pi. (1 point) 3 inches 4 inches 8 inches 16 inches

Respuesta :

zianebonankenotdbev
Volume of cube = 1/3 * pi * r^2 * h
83.74 = 1/3 x 3.14 x r^2 x 5 = 5.233r^2
r^2 = 83.74/5.233 = 16
r = sqrt(16) = 4

Answer: d = 2(4) = 8 inches.
JeanaShupp

Answer: 8 inches

Step-by-step explanation:

The volume of a cone is given by :-

[tex]\text{Volume}=\dfrac{1}{3}\pi r^2 h[/tex], where r is radius and h is height of the cone.

Given : The volume of cone = 83.74 cubic inches

The height of cone = 5 inches

Then by using the above formula , we have

[tex]83.74=\dfrac{1}{3}(3.14) r^2 5\\\\\Rightarrow\ r^2=\dfrac{3\times83.74}{3.14\times5}\\\\\Rightarrow\ r^2=16.0012738854\approx16\\\\\Righatrrow\ r=\sqrt{16}=4\text{ inches}[/tex]

Diameter of cone = [tex]2r=2(4)=8\text{ inches}[/tex]

Hence, the diameter of cone =  8 inches

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