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?
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 increase in volume is $\displaystyle {\pi}$ x 30 x 30 x 5 = 14137.19994 $\displaystyle cm^3.$
So the volume of the sphere is 14137.19994 $\displaystyle cm^3$
Volume Sphere = $\displaystyle \frac {4}{3}{\pi}r^3$
So 14137.19994 = $\displaystyle \frac {4}{3}{\pi}r^3$ - solving for r we get 15cm.
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$\displaystyle =\displaystyle\frac{4}{3}{\pi}r^3$
Volume of a cylindrical shape$\displaystyle ={\pi}R^2h$
To easily cancel terms...
$\displaystyle \displaystyle\frac{4}{3}{\pi}r^3={\pi}R^2h={\pi}30 ^2(5)$
$\displaystyle \displaystyle\ r^3=\frac{15(2)15(2)5(3)}{4}=\frac{15^2(15)4}{4}=1 5^3$