A cylindrical container holds three tennis balls, each with a diameter of 2.5 inches. The balls are stacked so they touch the container on the sides, top, and bottom. What is the volume of the empty space inside the container? Round your answer to the nearest hundredth, if necessary.

the volume of the empty space is

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, cylinder and sphere.

1. If we take a careful look at the problem, we will understand that the diameters of the four balls all sum up to give the height of the cylinder

2. Also to solve for the empty space, we have to subtract the volume of the 3 balls from the volume of the cylinder.

Given data

Diameter of sphere and cylinder d=  2.5 in

Radius r =  

Height h=  

let us solve for the volume of the cylinder

we can now solve for the volume of all three balls

we know that the volume of sphere is given as

since we are solving for 3 balls we multiply by 3

hence the volume of the empty space is

= volume of cylinder- volume of all three balls

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

just find the gcf and solve the gcf's until you get each answer i have a really good feeling somethings missing xd (like the dimensions of the fence) *cough *cough *hint *hint

step-by-step explanation: