Question

an ostrich egg has about the same volume as a sphere whith a diameter of 5 inches. If the eggshellis about 1/12 inch thick, find the volume of just the shell, not including the interior of the egg. Round your answer to the nerest tenth.

Answer 1

Volume of the shell is
`6.3\ in^3`.

Explanation:

Given:

diameter of the egg = 5 in

radius of the egg
`r = \frac12 * 5 = 2.5 \ in`

thickness of the shell =
`(1)/(12) \ in`

radius of interior without the shell =
`2.5 - (1)/(12) = (2.5* 12)/(12)- (1)/(12) = (30)/(12)- (1)/(12)= (30-1)/(12)=(29)/(12)\ in`

We need to find the volume of the shell.

Solution:

To find the volume of the shell we will subtract Volume of interior from Volume of the egg.

first we will find the Volume of the egg.

Now we know that;

egg is in spherical form so we will use Volume of sphere.

Volume of sphere is 4 by 3 times π times cube of the radius.

framing in equation form we get;

Volume of egg =
`(4)/(3)\pi r^3 = (4)/(3)\pi * 2.5^3 \approx 65.45\ in^3`

Volume of interior =
`(4)/(3)\pi r^3 = (4)/(3)\pi * ((29)/(12))^3 \approx 59.12\ in^3`

Volume of shell = Volume of egg - Volume of interior =
`65.45-59.12 = 6.33\ in^3`

Rounding to nearest tenth we get;

Volume of shell =
`6.3\ in^3`

Hence Volume of the shell is
`6.3\ in^3`.