volume of sphere

Question

One spherical concrete reservoir has its outer diameter equal to 4.6cm and the thickness of its wall is 20 cm. Find the capacity of the reservoir in litre.

Answer 1

Dear Sam,

     This problem will only work if the outer diameter =4.6 meters, not centimeters.  Otherwise, it just won't work. 

Question:  Find the capacity of the reservoir in liters.

 

Normally, a spherical concrete reservoir is made with a thick rubber balloon, which is inflated and concrete is placed around it. Therefore, the inner radius is from the center of the sphere to the inflated rubber balloon wall.  The outer radius is from the center to the outer area of the concrete wall. Disregard thickness of rubber balloon.  This is not the same kind of a balloon that children blow up; this might be $100,000 balloon depending on its diameter. There is a pipe entering it bringing the water into it, and a pipe exiting taking water to the customers.  Also, there is a little door that can be opened, so someone can clean the inside of it. Furthermore, it has an air vent.

 

 

Given:  outer diameter=4.6 M, so outer radius=D/2=4.6/2=2.3 M

 

    concrete wall thickness=20 cm     20cm/100 cm= 1/5 meter=.2 M

 

Change to meters, so that everything is in the same units.  To find the inner radius, subtract .2 M cement thickness

 

from 2.3 M outer radius:     2.3-.2=2.1= inner radius

 

 

 V=(4/3) *pi* r³ = (4/3)*π* (2.1)³   Volume of inner spherical container.

 

 

1000 L= 1 M³  , so  multiply 38.79238609 by 1,000.  Note: To multiply, just move the point three places to the right for the three places in 1,000.       

 

Answer:      38,792.38609 Liters   You may round it:   38,792.39 L

 

If I have helped you, please give me a thumbs up.

 

                                                                                    Susan C.