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A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is

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A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is

by M7MBA » Fri Jun 05, 2020 8:33 am

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A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

(A) \(\dfrac{16}{9\pi}\)

(B) \(\dfrac4{\pi}\)

(C) \(\dfrac{12}{\pi}\)

(D) \(\sqrt{\frac2{\pi}}\)

(E) \(4\sqrt{\frac2{\pi}}\)

[spoiler]OA=E[/spoiler]

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Re: A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container

by deloitte247 » Sat Jun 13, 2020 8:07 am
$$Volume\ of\ \ cylinder\ =\ \pi\ r^2h$$
Given that:
Cylinder is half full of water
Volume of 1/2 of water = 36 cubic inches
Container's volume = 36 * 2 = 72 cubic inches
Height = 9 inches
$$\frac{72}{\pi\cdot9}=\frac{\pi\ r^2\cdot9}{\pi\cdot9}\left(make\ r^2\ the\ subject\ of\ the\ formular\right)$$
$$r^2=\frac{72}{\pi\cdot9}$$
$$r^2=\frac{8}{\pi}$$
$$r=\sqrt{\frac{8}{\pi}}=\frac{\sqrt{8}}{\sqrt{\pi}}$$
$$r=\frac{2\sqrt{2}}{\sqrt{\pi}}$$
$$diameter\ =\ 2r$$
$$where\ r\ =\frac{2\sqrt{2}}{\sqrt{\pi}}$$
$$diameter\ =2\cdot2\frac{\sqrt{2}}{\sqrt{\pi}}$$
$$diameter\ =4\frac{\sqrt{2}}{\sqrt{\pi}}$$
$$=4\frac{\sqrt{2}}{\sqrt{\pi}}$$
$$Answer\ =\ E$$
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