Question

A cylindrical tub whose diamete is 12cm and height is 15cm is full of ice cream. whole ice cream is to be divided into 10 childrens in equal ice cream cone with conical base surmounted by a hemispherical top if the hieght of conical part is twice the diameter of its base . find the diameter of conical part ​

Answer 1

Answer:

The Diameter of the conical part is 6 cm.

Step-by-step explanation:

Given:

Diameter of cylindrical tub is 12 cm and height (h) is 15 cm.

To Find:

Diameter of conical part.

Solution:

∴ Radius(r) of the cylindrical tub = 12/2 = 6 cm.

∴Volume of cylindrical tub = πr²h

= π x 6² x 15 cm³

= π x 540 cm³

Let, radius of the conical part is R cm and diameter is D cm.

∴ Height = 2D = 4R

Now, Radius of the hemispherical part is (R1) = R [∵Conical base surmounted by a hemispherical top]

∴ Total volume of ice cream = Volume of Cone + Volume of Hemisphere

=$\frac{1}{3}\pi R^{2}4R+\frac{2}{3}\pi R^{3}$  [∵ Height = 2D = 4R]

=$\frac{1}{3}\pi R^{2}(4R+2R)$

=$\frac{1}{3}\pi R^{2}(6R)$

=$2\pi R^{2}R$

=$2\pi R^{3}$

∴ $10*2\pi R^{3}=\pi *540$   [∵Whole ice cream is to be divided into 10 children]

⇒$R^{3}=\frac{540}{20}$

⇒$R^{3}=27$

⇒$R=\sqrt[3]{27}$

⇒$R=3$ cm

∴ Diameter = 2 x Radius

= 2 x 3 cm

Diameter = 6 cm.

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