CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A cylindrical container is filled with ice-cream, whose diameter is $$12cm$$ and height is $$15cm$$. The whole ice-cream is distributed to $$10$$ children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.


Solution

Volume of cylindrical container$$=\pi { R }^{ 2 }H=\pi \times { 6 }^{ 2 }\times 15=540\pi ㎤$$
Let radius of base of conical portion be 'r', then diameter$$=2r$$
and height$$=2\times 2r=4r$$
$$10\times $$volume of each cone=volume of container
$$\Rightarrow 10\left[ \cfrac { 1 }{ 3 } \pi { r }^{ 2 }h+\cfrac { 2 }{ 3 } \pi { r }^{ 3 } \right] =540\pi \Rightarrow 10\times \cfrac { 1 }{ 3 } \pi \left[ { r }^{ 2 }\times 4r+2{ r }^{ 3 } \right] =540\pi $$
$$\Rightarrow 6{ r }^{ 3 }=162\Rightarrow { r }^{ 3 }=27\Rightarrow r=\sqrt [ 3 ]{ 27 } =3cm$$
$$\therefore $$Diameter $$=2r=2\times 3=6cm$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image