Question

A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3 cm.If the height of the toy is 12 cm, find the number of toys so formed.
​

Answer 1

Answer:

The Number of toys formed is 12.

Step-by-step explanation:

Given :  

Diameter of cylinder = 12 cm  

Radius of cylinder , R = 12/2 = 6 cm

Radius of hemisphere = Radius of the cone, r  = 3 cm

Height of the cylinder, H = 15 m

Height of the toy = 12 cm  

Height of cone, h = 12 - 3 = 9 cm

Volume of solid cylinder,V = πR²H

V = π× 6² × 15

V = π × 36 × 15

V of solid cylinder = 540π cm³

Volume of toy = Volume of hemisphere + Volume of cone

= (2/3πr³ + 1/3πr²h)

= ⅓ πr²(2r + h)

= ⅓ π × 3² (2 × 3 + 9)

= π/3 × 9 (6 + 9)

= 3π× 15  

= 45 π cm³

Volume of toy = 45 π cm³

Number of toys formed ,n = Volume of solid cylinder/Volume of toy

n = 540π/45π

n = 540/45

n = 12

Hence, the Number of toys = 12

Answer 2

Step-by-step explanation:

let the number of toys formed be 'n',

n× bol.of each toy= bol.of cylinder

$= > n \times ( \frac{1}{3}\pi \times {3}^{2} \times 9 + \frac{2}{3}\pi \times {3}^{3} ) = \pi \times {6}^{2} \times 15 \\ = > n \times \frac{\pi}{3}(81 + 54) = \pi \times 36 \times 15 \\ > = > n = \frac{36 \times15 \times 3 }{135} = 12$