Question

What is the answer to this?

Answer 1

Answer:

C. 97.6 in³

Step-by-step explanation:

The formula of a volume of a cylinder:

$V=\pi r^2H$

r - radius

H - height

We have

$2r=4\ in\to r=2\ in\\\\H=8\ in$

Substitute:

$V_1=\pi(2^2)(8)=\pi(4)(8)=32\pi\ in^3$

The formula of a volume of a cone:

$V=\dfrac{1}{3}\pi r^2H$

We have

$r=2\ in\\\\H=0.7\ in$

Substitute:

$V_2=\dfrac{1}{3}\pi(2^2)(0.7)=\dfrac{1}{3}\pi(4)(0.7)=\dfrac{1}{3}\pi(2.8)=\dfrac{2.8\pi}{3}=\dfrac{28\pi}{30}=\dfrac{14\pi}{15}\ in^3$

The volume of the plastic object:

$V=V_1-V_2$

$V=32\pi-\dfrac{14\pi}{15}=\dfrac{480\pi}{15}-\dfrac{14\pi}{15}=\dfrac{466\pi}{15}\\\\\pi\approx3.141\\\\V\approx\dfrac{466}{15}\cdot3.141\approx97.6$