Question

A cylindrical ice cream pot of radius 20 cm and height 60 cm is filled completely with ice cream. It was packaged in ready to sale cones of radius 2 cm and height 10 cm. How many such cones can be filled?

Answer 1

Hint: Ice cream is being transferred from a cylinder to cone. But the volume of ice cream will not change due to this transfer. Calculate the volume of ice cream when it was in the cylindrical pot. And then calculate the volume of one ice cream cone. That would help you get the number of cones you need to transfer complete ice cream from the cylindrical pot to the cones.

Complete step-by-step answer:
It is clear that the net volume of ice cream will not change.
Let us first calculate the volume of ice cream.
Since ice cream is filled in the cylindrical pot, the volume of the ice cream will be same as the volume of the cylindrical pot.
Let the volume of the cylinder be \[{V_{cy}}\]. Then, we will use the formula
 $ {V_{cy}} = \pi {R^2}H $
Where,
 $ R $ is the radius of the cylinder
And $ H $ is the height of the cylinder
It is given in the question that,
Radius of the cylinder, $ R = 20cm $
And height of the cylinder, $ H = 60cm $
Therefore, we get
 $ {V_{cy}} = \dfrac{{22}}{7} \times {20^2} \times 60 $ . . . (1)
Now, let the volume of one ice cream cone be $ {V_{co}} $ .
Then we can use the formula of volume of cone and write
 $\Rightarrow {V_{co}} = \dfrac{1}{3}\pi {r^2}h $
Where,
 $ r $ is the radius of the cone
And $ h $ is the height of the cone
It is given to us that,
Radius of the cone, $ r = 2cm $
And height of the cone, $ h = 10cm $
Then, the volume of one cone will be
 $\Rightarrow {V_{co}} = \dfrac{1}{3} \times \dfrac{{22}}{7} \times {2^2} \times 10 $ . . . (2)
Now, let us say, we need an $ n $ number of cones to transfer the complete volume of ice cream from the cylindrical pot to the ice cream cones. Then
 $ {V_{cy}} = n{V_{co}} $
Substitute the values from equations (1) and (2) into the above equation,
 $ \Rightarrow \dfrac{{22}}{7} \times {20^2} \times 60 = n \times \dfrac{1}{3} \times \dfrac{{22}}{7} \times {2^2} \times 10 $ . . . (3)
Simplifying it, we get
 $ n = 1800 $
Therefore, we will need 1800 cones to pack all the ice cream from the cylindrical cone.

Note: It is important to understand that the volume of ice cream will not change. The entire question is based on this fact. Sometimes after dividing the two volumes we might get decimals in such cases just round off the number to nearest value.