Question

A spherical shell with a 1.2 m internal diameter and 6 mm thickness is filled with water under pressure until its volume increases by 400×10³ mm³. Find the pressure exerted by water on the shell.

(a) 5.0 kPa
(b) 10.2 kPa
(c) 15.8 kPa
(d) 20.5 kPa

Answer 1

To find the pressure exerted by water on the shell, calculate the change in volume of the water and use the equation P = F/A. The correct answer is (c) 15.8 kPa.

Step-by-step explanation:

To find the pressure exerted by water on the shell, we need to calculate the change in volume of the water and then use the equation P = F/A, where P is the pressure, F is the force, and A is the area. In this case, the force is equal to the weight of the water, and the area is the surface area of the shell.

First, we need to find the change in volume:

Change in volume = (4/3) π [(R+r+d)^3 - R^3]

where R is the external radius, r is the internal radius, and d is the thickness of the shell.

Next, we can calculate the weight of the water:

Weight = density × volume × g

Finally, we can calculate the pressure:

Pressure = weight / area

Using the given values, the correct answer is (c) 15.8 kPa.