both cylinders are emptied, and water is poured into the narrow cylinder up to the 11th mark. how high would this water rise if it were poured into the empty wide cylinder

The height of the water when poured into the empty wide cylinder is;

Option A; To the 7¹/₃ mark

Formula for volume of a cylinder is;

V = πr²h

where;

r is radius

h is height

We are told that water is poured into the wide cylinder up to the 4th mark. Thus, for the wide cylinder, h = 4. Thus;

V_wide = 4πR²

Similarly, we are told that water is poured into the narrow cylinder up to the 6th mark. Thus, for the narrow cylinder, h = 6. Thus;

V_narrow = 6πr²

Now, the volume of the water will be the same since it was the same quantity that was poured. Thus;

V_wide = V_narrow

4πR² = 6πr²

⇒ R²/r² = 6/4

simplifies to get; R²/r² = ³/₂

Now both cylinder were emptied and water poured rises to the 11th mark for the narrow cylinder. Thus;

πR²H = 11πr²

R²/r² = 11/H

Earlier, we saw that R²/r² = ³/₂. Thus;

11/H = ³/₂

H = 22/3

H =  7¹/₃

The complete question is;

Attached are the drawings of a wide and a narrow cylinder. The cylinders have equally spaced marks on them. Water is poured into the wide cylinder up to the 4th mark (see A). This water rises to the 6th mark when poured into the narrow cylinder (see B). Both cylinders are emptied, and water is poured into the narrow cylinder up to the 11th mark. How high would this water rise if it were poured into the empty wide cylinder?

A) To the 7¹/₃ mark

B)To the 8th mark

C) To the 7¹/₂mark

D)To the 9th mark

E) To the 11th mark  

Read more at; brainly.com/question/16760517

Answer:

COMPLETE QUESTION:

To the right are drawings of a wide and a narrow cylinder. The cylinders have equally spaced marks on them. Water is poured into the wide cylinder up to the 4th mark (see A). This water rises to the 6th mark when poured into the narrow cylinder (see B). Both cylinders are emptied, and water is poured into the narrow cylinder up to the 11th mark. How high would this water rise if it were poured into the empty wide cylinder?

a)To the 7 1/2 mark b)To the 9th mark c)To the 8th mark d)To the 7 1/3 mark

e)To the 11th mark

ANSWER : Option D (To the 7 1/3 mark)

Step-by-step explanation:

First part of the question enables us to get the relationship between the radius of the wider cylinder (R) and the narrow cylinder(r) i.e

Volume of cylinders

π x R² x 4 = πxr²x 6

R²/r² = 6/4

after both cylinder were emptied

π x R² x h = π x r² x 11

R²/r² = 6/4 = 11/h

h = (4 x 11) /6 = 22/3 = 7 1/3 mark

Therefore, the height of the water in the wide cylinder is 7 1/3