# Math Help - Cylinder Question-Complicated

1. ## Cylinder Question-Complicated

A Cylinder has base of radius 7cm ...height 15cm.....it is a regular cylinder....

1.water is filled upto height of 10cm of this cylinder , find the volume of water...

Answer : v= 22/7 x 7 x 7 x 10
: volume of water=1540ml.

2.When 18 small spheres are put into this cylinder the water level rises up as "h"cm....Prove That h = 24a3(3=Cube) / 49

2. Originally Posted by hex
A Cylinder has base of radius 7cm ...height 15cm.....it is a regular cylinder....

1.water is filled upto height of 10cm of this cylinder , find the volume of water...

Answer : v= 22/7 x 7 x 7 x 10
: volume of water=1540ml.

2.When 18 small spheres are put into this cylinder the water level rises up as "h"cm....Prove That h = 24a3(3=Cube) / 49

first the sphere's must be identitical or this doesn't work...

The Volutme of a sphere is $V=\frac{4}{3}\pi r^3 \mbox{ cm}^3$ where r is the radius.

So the Volume of 18 is $24\pi r^3 \mbox{ cm}^3$

The volume of a right circlular cylindar is $V=\pi r^2 h$ and we know that r in the cylindar is 7 cm so we get

$24\pi r^3 \mbox{ cm}^3=49 \pi h \mbox{ cm}^2$

Now we solve for h to get

$h=\frac{24\pi r^3 \mbox{ cm}^3}{49 \pi \mbox{ cm}^2}=\frac{24 r^3}{49} \mbox{ cm}$