Question

solid cylinder of diameter 12cm and height 15cm is melted and recast into 12 toys in the shape of right circular cone mounted on a hemisphere. find the radius of a hemisphere and total heisght of a toy if height of a conical part is three times its radius?

Answer 1

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, 
Radius of hemisphere = Radius of the cone
From the given information.
h = 3r
Volume of cylinder = Volume of hemisphere + Volume of 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, height of the toy = 3 × 3
= 9 cm
Answer.

Answer 2

Answer:

Step-by-step explanation:

cylinder       cone              hemissphere

r=6              r=3                r=3

h=15           h=12-3=>9

volume of cylinder =[ volume of cone +volume of hemisphere]nos. of toys

=>πx36x15=2/3xπx27 + 1/3xπx9x9x n

=>πx36x15=1/3xπ[54+81]x n

=>36x15x3=135x n

=>12=n