# A metallic cylinder has radius 3cm and height 5 cm. To reduce its weight a conical hole is drilled in the cylinder. The conical hole has a radius of 3/2 cm and it's depth is 8/9cm. Calculated the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical

1
by Jaanus

2016-04-12T01:14:47+05:30

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Given:
cylinder: radius 3cm and height 5cm

volume of a cylinder = π r² h
v = 3.14 * (3cm)² * 5cm
v = 3.14 * 9cm² * 5cm
v = 141.3 cm³

conical hole: radius 3/2 cm and depth 8/9 cm

volume of a cone = π r² h/3
v = 3.14 * (3/2cm)² * 8/9cm ÷ 3
v = 3.14 * 9/4 cm² * 8/27 cm
v =  (3.14 * 9 * 8) / (4*27)
v = 226.08 / 108
v = 2.09 cm³

volume of the metal left: 141.3 cm³ - 2.09 cm³ = 139.21 cm³