Question

Four circular cylindrical vessels, each having a diameter 21 cm and height 38 cm are full of ice-cream. This ice-cream is to be filled in cones each of height 12 cm and diameter 7 cm, having a hemispherical shape on the top. Find the total number of cones that can be filled with the ice-cream. 50 POINTS!!!

Answer 1

$\huge{\mathfrak{Solution}}$


Volume of a right circular cylinder = 4/3πr²h

Volume of hemisphere = 2/3πr²

Volume of cone = Volume of cylinder + Volume of hemisphere = 1/3πr²h + 2/3πr²

Given, Volume of right circular cylinder = n [Volume of cone + Volume of hemisphere]

Therefore, 4/3πr²h = n [1/3πr²h + 2/3πr² ]

Implies, π x 21² x 38 = n π / 3 x 7² / 4 [12 + 2 x 7 / 2]

Implies, 21 x 21 x 38 = (n x 7 x 7) / 12 x 19

Implies, n = (21 x 21 x 38 x 12) / (7 x 7 x 19) = 216

Answer 2

$\huge\bf\mathcal\pink{SOLUTION}$

let the no. of cones be n
CYLINDER
h = 38 cm
d = 21 cm
so... r = 21/2 cm
volume of cylinder = pi x r^2h
CONE
h = 12 cm
d = 7 cm
so, r = 7/2 cm
volume of cone = 1/3 x pi x r^2h
HEMISPHERE
d = 7 cm
so, r = 7/2 cm
volume of hemisphere = 2/3 x pi x r^3
so........

volume of n cones = volume of  4 cylinders
n x volume of  1 cone + volume of hemisphere = volume of 4 cylinders
n x 1/3 pi x r^2h  +  2/3 x pi x r^3 = 4 x pi x r^2h

n x pi r^2( 1/3h + 2/3r ) = 4 x pi r^2h

n x r^2(1/3h + 2/3r )  = 4 x r^2h    ....(pi will get cancelled )

n x (7/2)^2 (1/3 x 12 + 2/3 x 7/2) = 4 x 21/2 x 21/2 x 38

n x  49/4  (4 + 7/3)  = 21 x 21 x 38

n x 49/4 x 19/3 = 21 x 21 x 38

n =  21 x 21 x 38 x  4 x 3 /  49 x 19

n = 3 x 3 x 2 x 4 x 3

n = 216
thus....the number of cones to be filled wid ice cream is 216

HOPE IT HELPS ❤❤