A right circular cylinder having diameter 12cm and height 15cm is full of icecream.The icecream is to be filled in identical cones of height 12cm and diameter 6cm having a hemispherical shape on the top.Find the number of cones required
Answers
CYLINDER CONE HEMISPHERE
d=12cm d= 6cm d=6cm
r= 6cm r= 3cm r= 3cm
h=15cm h=12cm
VOLUME OF ICE CREAM= πr²h= 22/7 ×6×6×15= 22×36×15/7 . cm³
VOLUME OF ICE CREAM THAT CAN BE FILLED IN THE CONE=
VOLUME OF CONE + VOLUME OF HEMISPHERE
= πr²h/3 + 2πr³/3
=πr²/3 (h + 2r)
= 22/7 × 3×3×1/3( 12+6)=22/7 ×3×18 cm³
n×volume of ice cream filled in one cone= volume of ice cream in the cylinder
n×22/7 ×3×18=22×36×15/7
n= 22×36×15/7 ×7/22×3×18
= 10 cones
#ANSWERWITHQUALITY
Answer:
the number of cones required is 10
Step-by-step explanation:
We need to get the amount of ice cream in the right circular cylinder.
We do this by getting the volume of the cylinder.
The volume of the cylinder is given by:
Volume = πr²h
Substituting we have:
Vol = π × (12/2)² × 15 = 540π cm³
Let's now get the volume of the cones
For the cones, we have the conical part and the hemispherical part.
So, the volume of a cone is:
Vol = Volume of the conical part + Volume of the hemispherical top
= 1/3π × (6/2)² × 12 + 2/3π × (6/2)³
= 36π + 18π = 54π cm³
Now that we have the volume of the ice cream, and the capacity of each cone, we can get the number of cones filled with ice cream.
The number of cones = 540π/54π = 10 cones
We need 10 cones of ice cream.