## OG A container in the shape

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### OG A container in the shape

by AbeNeedsAnswers » Tue Jul 25, 2017 8:21 pm

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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) 16/9Ï€

(B) 4/(root)Ï€

(C) 12/(root)Ï€

(D) (root)(2/Ï€)

(E) 4(root)(2/Ï€)

E

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by [email protected] » Tue Jul 25, 2017 8:47 pm
AbeNeedsAnswers wrote: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) 16/9Ï€

(B) 4/(root)Ï€

(C) 12/(root)Ï€

(D) (root)(2/Ï€)

(E) 4(root)(2/Ï€)

E
Given that the cylinder is half full and the volume of water in the cylinder is 36 cubic inches, thus, the volume of the cylinder = 2*36 = 72 cubic inches.

We know that the volume of a cylinder = Ï€r^2h

=> Ï€r^2h = 72

= 9Ï€r^2 = 72; given that height = h = 9 inches

= Ï€r^2 = 8

= r^2 = 8/Ï€

= r = âˆš(8/Ï€)

Diameter of the cylinder = 2r = 2âˆš(8/Ï€) = 4âˆš(2/Ï€)

Hope this helps!

-Jay
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by [email protected] » Mon Aug 14, 2017 2:08 pm
AbeNeedsAnswers wrote: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) 16/9Ï€

(B) 4/(root)Ï€

(C) 12/(root)Ï€

(D) (root)(2/Ï€)

(E) 4(root)(2/Ï€)

E
Recall that the volume of a cylinder is:

Since half of the capacity of the cylinder is 36, the full capacity of the cylinder is 72; thus:

72 = Ï€r^2(9)

8/Ï€ = r^2

âˆš(8/Ï€) = r

âˆš8/âˆšÏ€ = r

(2âˆš2)/âˆšÏ€ = r

2âˆš(2/Ï€) = r

The diameter is twice the radius. Thus, the diameter is 2 x 2âˆš(2/Ï€) = 4âˆš(2/Ï€).

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### Re: OG A container in the shape

by [email protected] » Sun Apr 18, 2021 3:28 pm
Hi All,

We’re told that a cylindrical tank (re: a cylinder/tube) is HALF full of water and contains 36 cubic inches of water (with the height of the CONTAINER equaling 9 inches). We’re asked for the DIAMETER of the base of the cylinder in inches.

Volume of a cylinder is (pi)(Radius^2)(Height), so we can use that formula – along with what we know about the water – to figure out the radius and diameter of the tank… It’s important to note that while the Height of the cylinder is 9 inches, the water reaches HALF of that height (meaning that the height of the water is 4.5 inches). Since the answers are all written as fractions, we should write that 4.5 as 9/2…

V = (pi)(R^2)(H) =
36 = (pi)(R^2)(9/2)

We can ‘cancel out’ the 9/2 by multiplying both sides by 2/9…

72/9 = (pi)(R^2)
8/pi = R^2
R = square root of (8/pi), which can be rewritten as 2[square root of (2/pi)]. Since the diameter is TWICE the radius, the diameter is 2(2[square root of (2/pi)] = 4[square root of (2/pi)]