Question

a container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream the ice cream is to be filled into a cone of height 12cm and diameter 6 CM having a hemispherical shape of the top find the number of such cones which can be filled with ice cream​

Answer 1

Given : Diameter of Cylinder = 12 cms

Radius of cylinder = 6cms

Height of Cylinder = 15 cms

Height of Cone = 12cms

Diameter of Cone = 6cms

Radius of Cone =3cms

To find : Number of cones to be filled(N)

Solution:

Step 1: Volume of Cylinder =

$\pi {r}^{2} h$

=π×6^2×15 cubic cms

Step 2: Volume of Cone =

$\frac{1}{3} \pi {r}^{2} h$

= (1/3)π3^2×12 cubic cms

Step 3: Volume of hemisphere=

$\frac{2}{3} \pi {r}^{3}$

= 2/3 π 3^3 cubic cms

Step 4: Volume of Cylinder = N×(Volume of Cone +Hemisphere)

=> π×6^2×15=N× { (1/3)π3^2×12 + 2/3 π 3^3 }

=> N=10

Hence, A total of 10 cones can be filled

Answer 2

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Step-by-step explanation:

1. let the height and radius of cylinder be h1 and r1.

∴ height of cylindrical container = 15cm

radius of cylindrical vessel      = 12/2 = 6cm

2. let the height and radius of cone be h2 and r2

height of cone = 12cm

radius of cone = 6/2 = 3cm

let n no. of ice creams be filled with ice cream of the container,

3. volume of ice cream cylinder = n x volume of 1 cone

⇒ π × r1² × h1 = n [1/3π × r2² × h2 + 2/3π × r2³]

⇒ π x 6² x 15 = n [1/3π x 3² x 12 + 2/3π x 3³

⇒    36 x 15    = n[36+18]

⇒ n = 36 x 15/54

∴ n = 10

hence, no of ice cream cones filled with ice cream are 10