A solid Aluminium metal hemispherical bowl of radius 30 cm. is melted down and cast into cylinder of radius 5 cm. and height 2 cm. How many cylinders can be cast from the solid metal?
Mensuration- Conversion of Solid from One Shape to Another
1 Answers
Do you know the formula for the volume of a sphere of radius $r$? If not, can you find the formula somewhere? Then you can divide it by $2$, to get the volume of a hemispherical bowl of radius $r$, and then you can let $r=30$ to get the volume of the bowl in the problem. Let's call it $V$.
Do you know the formula for the volume of a cylinder of radius $s$ and height $h$? If not, can you find the formula somewhere? Then you can put in $s=5$ and $h=2$ to find the volume of each cylinder. Let's call it $W$.
Now if you know the volume $V$ of the hemisphere, and you know the volume $W$ of each cylinder, can you figure out how many cylinders you can make from the hemisphere?
EDIT: Well, it has been over a month, so I suppose the statute of limitations has run out, and I can supply details. The volume of a sphere is $(4/3)\pi r^3$, so the volume of a hemisphere is $(2/3)\pi r^3$. With $r=30$ the volume of the bowl is $V=18000\pi$.
The volume of a cylinder is $\pi s^2h$, so with $s=5$ and $h=2$ we get $W=50\pi$.
So the number of cylinders you can make is $V/W=(18000\pi)/(50\pi)=360$.