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:

SOLUTION :

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 formed is 12.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\huge \red{ \star \: {heya \: \star}}$

here is ur answer ➖➖➖➖➖➖➖➖➖➖➖➖➖⬇


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


hope it helps you...

please mark as a brainliest ✌❤☺☺