Cylindrical tank

**Natasha1** · October 25th 2010, 12:16 PM

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?

**brennan** · October 25th 2010, 12:34 PM

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.

**Archie Meade** · October 25th 2010, 01:03 PM

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?

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...

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

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

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