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Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.
Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm. a. What is the volume of the cylinder? Explain your method for finding the volume.
b. What is the total volume of the three balls? Explain your method for finding the total volume.
c. What percent of the volume of the container is occupied by the three balls? Explain how you would find the percent.
We know the following:Cylinder volume: V₁ = π r² hBall (sphere) volume:V₂ =π r³where:V - volumer - radius of base of cylinder and diameter of ballh - height of cylinder.R = 13 cm ⇒ r = 13 ÷ 2 = 6.5π = 3.14a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:h = 3 × r = 3 × 13 cm = 39 cmr = 6.5 cmSo,V₁ =π r² hV₁ =3.14 × (6.5 cm)² × 39 cmV₁ = 5,173.9 cm³b. The total volume of three balls is the sum of volumes of each ball:Vₐ = 3 ×V₂Vₐ = 3 ×π r³Vₐ = 3 ×3.14(6.5 cm)³Vₐ = 3,449.3 cm³c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:V =×100V =×100V = 0.6666 ×100V = 66.66%...