a container shaped like a right circular cylinder having diameter 14 cm and height 20 cm full of ice cream.the ice cream is to be filled into cones of height 7cm and diameter 4 cm having a hemispherical shape on the top .find the number of such cones which can be filled with ice cream .
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Subject:
Math -
Author:
alfonsoharris -
Created:
1 year ago
Answers 1
Step-by-step explanation:
Height (h
1
) of cylindrical container = 15 cm
Radius =
2
Diameter
Radius (r
1
) of circular end of container =
2
12
=6 cm
Radius (r
2
) of circular end of ice-cream cone =
2
6
=3 cm
Height (h
2
) of conical part of ice-cream cone = 12 cm
Let n ice-cream cones be filled with ice-cream of the container.
Volume of ice-cream in cylinder = n (Volume of 1 ice-cream cone + Volume of hemispherical shape on the top)
πr
1
2
h
1
=n(
3
1
πr
2
2
h
2
+
3
2
πr
2
3
)
⇒π×6
2
×15=n(
3
1
π3
2
×12+
3
2
π3
3
)
⇒n=
3
1
×9×12+
3
2
×27
30×15
⇒n=
108+54
36×15×3
n=10
So, 10 ice-cream cones can be filled with the ice-cream in the container.
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sam27
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