Respuesta :
Answer:
Volume of the shell is [tex]6.3\ in^3[/tex].
Step-by-step explanation:
Given:
diameter of the egg = 5 in
radius of the egg [tex]r = \frac12 \times 5 = 2.5 \ in[/tex]
thickness of the shell = [tex]\frac{1}{12} \ in[/tex]
radius of interior without the shell = [tex]2.5 - \frac{1}{12} = \frac{2.5\times 12}{12}- \frac{1}{12} = \frac{30}{12}- \frac{1}{12}= \frac{30-1}{12}=\frac{29}{12}\ in[/tex]
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 = [tex]\frac{4}{3}\pi r^3 = \frac{4}{3}\pi \times 2.5^3 \approx 65.45\ in^3[/tex]
Volume of interior = [tex]\frac{4}{3}\pi r^3 = \frac{4}{3}\pi \times (\frac{29}{12})^3 \approx 59.12\ in^3[/tex]
Volume of shell = Volume of egg - Volume of interior = [tex]65.45-59.12 = 6.33\ in^3[/tex]
Rounding to nearest tenth we get;
Volume of shell = [tex]6.3\ in^3[/tex]
Hence Volume of the shell is [tex]6.3\ in^3[/tex].
