Answer:
Expression: [tex]\pi(\frac{D}{2})^{2}h-\pi(\frac{d}{2})^{2}h[/tex]
Volume: [tex]339.29cm^{3}[/tex]
Step-by-step explanation:
The formula for the volume of a cylinder is: [tex]\pi r^{2}h[/tex]. Since we are given the diameters instead of the radius, we divide the diameters by 2 to get the radius.
∴ The expression for the volume of the large cylinder after the hole was removed is [tex]\pi (\frac{D}{2})^{2}h - \pi(\frac{d}{2})^{2}h[/tex]
Approximate volume:
Substitute the numbers in:
[tex]\pi(\frac{8}{2})^{2}\times9-\pi(\frac{4}{2})^{2}\times9=339.29cm^{3}[/tex] (to the second decimal place)
∴ The volume of the big cylinder after removing the cylindrical hole is approximately [tex]339.29cm^{3}[/tex]
