Question

IN NEED OF A MATH WIZ!!!!!

Answer 1

The unoccupied volume will be the volume of the can minus the volume of the three tennis balls.

V=HπR^2-3(4πr^3)/3

V=HπR^2-4πr^3  where H=height of can, R=radius of can, r=radius of ball

We are told H=7, R=1.5, and r=1.125  (2.25/2=d/2=r) so

V=7π1.5^2-4π1.125^3

V=15.75π-5.6953125π  in^3

V≈31.58 in^3

Answer 2

Answer: $31.58\ inches^3$

Step-by-step explanation:

Given: The diameter of tennis ball = 2.25 inches

The radius of ball =$\frac{2.25}{2}=1.125\ inches$

The volume of ball (sphere) is given by :-

$V=\frac{4}{3}\pi r^3\\\\\Rightarrow V=\frac{4}{3}(3.14)(1.125)^3\\\\\Rightarrow\ V=5.96109375\approx5.96\ inch^3$

For cylindrical canister, Height = 7 inches

Radius = 1.5 inches

The volume of  cylindrical canister (cylinder) is given by :-

$V=\pi r^2h\\\\\Rightarrow V=(3.14)(1.5)^2(7)\\\\\Rightarrow\ V=49.455\approx49.46\ inch^3$

Now, the canister’s volume is unoccupied by tennis balls

= Volume of canister - volume of 3 balls

=$49.46-3(5.96)=49.46-17.88=31.58\ inches^3$

Hence, the canister’s volume is unoccupied by tennis balls=$31.58\ inches^3$