Question

a solid cylinder of diameter 12cm and 15 cm is melted and recast into 12 toysin the shape of the right circular cone mounted on a hemisphere find the radius of the hemisphere and the total height of The Toy if height of the conical part is 3 times its radius

Answer 1

Answer:

9 cm

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Solution:-

Given :  

Diameter of cylinder = 12 cm  

So, the radius = 12/2 = 6 cm

Height of the cylinder = 15 m

Let 'h' be the total height and 'r' the radius of the hemisphere respectively.

Now,  

The Radius of hemisphere = Radius of the cone

From the given information.

h = 3r

The Volume of cylinder = Volume of hemisphere + Volume of a cone

πr1²h = 12 × (2/3πr³ + 1/3πr²h)

⇒ π(6)²*15 = 12π × {2/3r³ + 1/3r²(3r)}

⇒ 36*15 = 12 × (2/3r³ + r³)  

⇒ 36*15 = 12 × (5r³/3)

⇒ 540 = (60r³/3)

⇒ 540 = 20r³

⇒ r³ = 540/20

⇒ r³ = 27

⇒ r = ∛27

r = 3 cm

Now, the radius of the hemisphere is 3 cm.

Therefore, the height of the toy = 3 × 3

= 9 cm

Answer.

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