# Cylindrical tank

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• October 25th 2010, 12:16 PM
Natasha1
Cylindrical tank
A cylindrical tank has a radius of 30cm and a height of 45cm. The tank contains water to a depth of 36cm.

A metal sphere is dropped into the water and is completely covered. The water level rises by 5cm.

What is the radius of the metal sphere? (Headbang)
• October 25th 2010, 12:34 PM
brennan
The increase in volume is ${\pi}$ x 30 x 30 x 5 = 14137.19994 $cm^3.$

So the volume of the sphere is 14137.19994 $cm^3$

Volume Sphere = $\frac {4}{3}{\pi}r^3$

So 14137.19994 = $\frac {4}{3}{\pi}r^3$ - solving for r we get 15cm.
• October 25th 2010, 01:03 PM
Archie Meade
Quote:

Originally Posted by Natasha1
A cylindrical tank has a radius of 30cm and a height of 45cm. The tank contains water to a depth of 36cm.

A metal sphere is dropped into the water and is completely covered. The water level rises by 5cm.

What is the radius of the metal sphere? (Headbang)

The water level rise has a "cylindrical shape" as the water is inside a cylinder.
The water rises by the volume of the sphere.

Volume of a spherical shape $=\displaystyle\frac{4}{3}{\pi}r^3$

Volume of a cylindrical shape $={\pi}R^2h$

To easily cancel terms...

$\displaystyle\frac{4}{3}{\pi}r^3={\pi}R^2h={\pi}30 ^2(5)$

$\displaystyle\ r^3=\frac{15(2)15(2)5(3)}{4}=\frac{15^2(15)4}{4}=1 5^3$