Cylinder - Geometry

[doclkk]

A certain right circular cylinder has a radius of 5 inches. There is a kind of liquid filled in this cylinder to the height of 9 inches. If this liquid is poured completely into a second right cylinder, then the liquid will fill the second cylinder to the height of 4 inches. What is the radius of the second cylinder, in inches?

A. 6
B. 6.5
C. 7
D. 7.5
E. 8

(D)

What was your thinking for logic?

[ssmiles08]

you can find the solution by a straight plug in of the formula.

Volume of cylinder = 2*pi*r^2*h

assume, the liquid is filled to the capacity for both cylinders.

V of 1st cylinder = 450*pi

V of 2nd cylinder = 2*pi*r^2*4

450*pi = 8*pi*r^2

225/4 = r^2

sqrt both sides = 15/2 ~ 7.5 (D)

[PussInBoots]

p * 25 * 9 = p * x^2 * 4
x^2 = 25 * 9 /4 => x = 5 * 3 / 2

[maihuna]

A certain right circular cylinder has a radius of 5 inches. There is a kind of liquid filled in this cylinder to the height of 9 inches. If this liquid is poured completely into a second right cylinder, then the liquid will fill the second cylinder to the height of 4 inches. What is the radius of the second cylinder, in inches?

A. 6
B. 6.5
C. 7
D. 7.5
E. 8

Area of cylinder = pi*r^2*h = pi*r1^2*h1
=> r1 = r*sq(h/h1)
=> r1 = 5*sq(9/4) = 5*3/2 = 7.5
Given

[Jeff@TargetTestPrep]

A certain right circular cylinder has a radius of 5 inches. There is a kind of liquid filled in this cylinder to the height of 9 inches. If this liquid is poured completely into a second right cylinder, then the liquid will fill the second cylinder to the height of 4 inches. What is the radius of the second cylinder, in inches?

A. 6
B. 6.5
C. 7
D. 7.5
E. 8

Let's find the volume of the liquid in the first cylinder:

V = πr^2 * h = π(5)^2 * 9 = 225π cubic inches

Now we can let x = radius of the second cylinder and solve for x by setting the volume of the liquid in the second cylinder equal to 225Ï€:

Ï€x^2 * 4 = 225Ï€

x^2 * 4 = 225

x^2 = 225/4

x = √(225/4)

x = 15/2

x = 7.5

Answer: D