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OG A container in the shape

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG A container in the shape

Post Tue Jul 25, 2017 8:21 pm
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) 16/9π

(B) 4/(root)π

(C) 12/(root)π

(D) (root)(2/π)

(E) 4(root)(2/π)

E

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Post 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) 16/9π

(B) 4/(root)π

(C) 12/(root)π

(D) (root)(2/π)

(E) 4(root)(2/π)

E
Recall that the volume of a cylinder is:

volume = π(radius)^2(height)

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

72 = πr^2(9)

8/π = r^2

√(8/π) = r

√8/√π = r

(2√2)/√π = r

2√(2/π) = r

The diameter is twice the radius. Thus, the diameter is 2 x 2√(2/π) = 4√(2/π).

Answer: E

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Post 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) 16/9π

(B) 4/(root)π

(C) 12/(root)π

(D) (root)(2/π)

(E) 4(root)(2/π)

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 = πr^2h

=> πr^2h = 72

= 9πr^2 = 72; given that height = h = 9 inches

= πr^2 = 8

= r^2 = 8/π

= r = √(8/π)

Diameter of the cylinder = 2r = 2√(8/π) = 4√(2/π)

The correct answer: E

Hope this helps!

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