Answer:
C. 97.6 in³
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have
[tex]2r=4\ in\to r=2\ in\\\\H=8\ in[/tex]
Substitute:
[tex]V_1=\pi(2^2)(8)=\pi(4)(8)=32\pi\ in^3[/tex]
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
We have
[tex]r=2\ in\\\\H=0.7\ in[/tex]
Substitute:
[tex]V_2=\dfrac{1}{3}\pi(2^2)(0.7)=\dfrac{1}{3}\pi(4)(0.7)=\dfrac{1}{3}\pi(2.8)=\dfrac{2.8\pi}{3}=\dfrac{28\pi}{30}=\dfrac{14\pi}{15}\ in^3[/tex]
The volume of the plastic object:
[tex]V=V_1-V_2[/tex]
[tex]V=32\pi-\dfrac{14\pi}{15}=\dfrac{480\pi}{15}-\dfrac{14\pi}{15}=\dfrac{466\pi}{15}\\\\\pi\approx3.141\\\\V\approx\dfrac{466}{15}\cdot3.141\approx97.6[/tex]
