Question

Solve this 36th Question (◍•ᴗ•◍)❤​

Answer 1

Question :

A solid cylinder of diameter 12 cm and the height 15 cm is melted and recast into 12 toys which are in the shape of right circular cone mounted on a hemisphere. If the height of the conical part is 3 times its radius, find the total height of the toy and the radius of the hemisphere.

Given :

• A solid cylinder of diameter 12 cm and the height 15 cm is melted and recast into 12 toys which are in the shape of right circular cone mounted on a hemisphere.
• The height of the conical part is 3 times its radius.

To find :

• Radius of the hemisphere.
• Total height of the toy.

Solution :

• Diameter of cylinder = 12 cm

Then,

• Radius of cylinder = 12/2 = 6 cm

• Height of cylinder = 15 cm

Therefore,

Volume of the cylinder = πr²h

$\to\sf{Volume\:_{cylinder}=\dfrac{22}{7}\times\:6\times\:6\times\:15\:cm^3}$

A/Q,

$\sf{Volume\:of\: cylinder=volume\:of\:12\: toys}$

Then,

$\to\sf{Volume\:of\:12\: toys=\dfrac{22}{7}\times\:6\times\:6\times\:15\:cm^3}$

$\to\sf{Volume\:of\:1\:toy=\dfrac{22}{7}\times\:6\times\:6\times\:15\times\dfrac{1}{12}\:cm^3}$

$\to\sf{Volume\:of\:1\: toy=\dfrac{11\times\:15\times\:6}{7}\:cm^3}$

Consider,

• Radius of the conical part = r cm

Therefore ,

• Height of the conical part = 3r cm

$\sf{Radius\:_{cone}=Radius\:_{hemisphere}=r\:cm}$

$\bold{Volume\:_{cone}=\dfrac{1}{3}\pi\:r^2h}$

$\implies\sf{Volume\:_{cone}=\dfrac{1}{3}\pi\:r^2\times\:3r\:cm^3}$

$\implies\sf{Volume\:_{cone}=\pi\:r^3\:cm^3}$

&,

$\bold{Volume\:_ {hemisphere}=\dfrac{2}{3}\pi\:r^3\:cm^3}$

Volume of conical part + Volume of hemisphere = Volume of 1 toy

According to the question :-

$\to\sf{\pi\:r^3+\dfrac{2}{3}\pi\:r^3=\dfrac{11\times\:15\times\:6}{7}}$

$\to\sf{\pi\:r^3(1+\dfrac{1}{3})=\dfrac{11\times\:15\times\:6}{7}}$

$\to\sf{\pi\:r^3\times\dfrac{5}{3}=\dfrac{11\times\:15\times\:6}{7}}$

$\to\sf{r^3=\dfrac{11\times\:15\times\:6}{7}\times\dfrac{3}{5}\times\dfrac{7}{22}}$

$\to\sf{r^3=27}$

$\to\sf{r=3}$

Therefore , radius of the hemisphere is 3 cm.

Then,

• Height of the conical part = 3×3 = 9 cm.

Height of hemisphere = Radius of hemisphere = 3 cm.

Therefore,

$\to\sf{Total\: height\:of\:the\:toy=Height\:of\: conical\:part+Height\:of\: hemisphere}$

$\to\sf{Total\:height\:of\:the\:toy=(9+3)\:cm}$

$\to\sf{Total\:height\:of\:the\:toy=12\:cm}$

Therefore, total height of the toy is 12 cm.

Answer 2

Step-by-step explanation:

sorry niharika as i am not using much phone so i hadnt answered any question of urs and its there and i will answer other question

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