What is the height of the cylinder?

Geometry Level pending

A cylinder has a base diameter of 1.5m. The height of liquid in the cylinder is 2.8m. A spherical ball with radius 0.44m is submerged causing the water to move up. The height of liquid and height of cylinder are now equal. What is the height of the cylinder? round your answer to the nearest meter

see my set : Marvin's Geometry Set

3 m 4 m 5 m 6 m

A Former Brilliant Member by A Former Brilliant Member

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1 solution

considering the sphere,

V s Vs = 4 3 \frac{4}{3} π π r 3 r^3 = 4 3 \frac{4}{3} ∗ π *π ∗ 0.4 4 3 *0.44^3 = 0.36 m 3 0.36 m^3

considering the cylinder,

0.36 m 3 = 0.36 m^3 = π π r 2 r^2 x x

0.36 m 3 = 0.36 m^3 = π π ∗ 0.7 5 2 *0.75^2 x x

x = 0.2 m x = 0.2 m

h e i g h t o f t h e c y l i n d e r = 2.8 + 0.2 = 3 m height of the cylinder = 2.8 + 0.2 = 3m

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The answer can be guessed quite easily since the next possibility, 4, is so far away. It would have been better to actually ask for the figure, to two decimal places, rather than rounded.

Marta Reece - 3 years ago

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