Water in a cylinder

Geometry Level 2

A right circular cylinder with base diameter of 4 and height of 12 is full of water. Three identical spherical balls each with diameter of 4 is slowly placed in this cylinder. What is the volume of the remaining water in this cylinder?

16 π 16\pi 21 π 21\pi 18 π 18\pi 14 π 14\pi

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1 solution

Vu Vincent
Feb 16, 2018

The cylinder volume is π r 2 h = π × 2 2 × 12 = 48 π \pi r^2 h = \pi \times 2^2 \times 12 = 48\pi

The volume of 3 spheres is 3 ( 4 3 π r 3 ) = 4 π r 3 = 4 π ( 2 ) 3 = 32 π 3(\frac{4}{3} \pi r^3) = 4 \pi r^3 = 4 \pi (2)^3 = 32\pi

So the remaining volume is 48 π − 32 π = 16 π 48\pi - 32\pi = \boxed{16\pi}

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