Question

a cylindrical container is filled with ice cream whose diameter is 12 cm and height is 15 CM the whole ice cream is distributed to 10 children in equal cones filled making hemispherical tops if the height of conical portion is twice than the diameter of its base find the diameter of the ice cream cone

Answer 1

Please see the attachment

Answer 2

Answer:

Diameter of the ice cream cone will be 6cm

Step-by-step explanation:

Let r, h be the radius and height of the cylindrical container, it is given that diameter=12cm, then r will be equal to 6cm.

Now, ,volume of the cylindrical container=${\pi}r^{2}h$

=${\pi}(6)^{2}15$=${\pi}(36)(15)$

=$540{\pi}$

Volume of 10 ice cream cones is = $540{\pi}$, then

Volume of 1 ice cream cone will be=$54{\pi}$

Volume of the cone will be given as:$\frac{2}{3}{\pi}R^{3}+\frac{1}{3}{\pi}R^{2}H$=$54{\pi}$, where R and H is the radius and height of the hemispherical cone.

Also, it given that H=2D, therefore, H=2(2R)=4R

⇒Volume=$\frac{2}{3}R^{3}+\frac{1}{3}R^{2}(4R)=54$

⇒$6R^{3}=162$

⇒$R^{3}=27$

⇒$R=3cm$

Therefore, diameter of the ice cream cone is= 2R=2(3)=6cm