Solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm find the internal diameter.
Answers
Answer:
6 cm
Step-by-step explanation:
Given:
Diameter of cone d = 14 cm.
Then, radius = d/2 = 7 cm.
height = 8 cm.
(i) Volume of cone:
= (1/3) πr²h
= (1/3) * π * (7)² * 8
= (392/3)π cm³
(ii)
Given, External diameter of the sphere = 10 cm.
Then, external diameter of the sphere R = 5 cm.
Volume of the hollow sphere:
= (4/3)π[R³ - r³]
= (4/3)π[5³ - r³]
= (4/3)π[125 - r³]
Now,
Volume of the hollow sphere = Volume of the cone
⇒ (4/3)π[125 - r³] = (392/3)π
⇒ (4)[125 - r³) = 392
⇒ 125 - r³ = 98
⇒ r³ = 27
⇒ r = 3
Therefore, Internal diameter of the sphere = 2r = 6 cm.
Hope it helps!
Diameter of cone=14 cm
so, Radius of cone= 7cm
Height of cone= 8cm
∴ Volume of cone= 1/3*pi*r^2*h
=1/3*pi*49*8 cm^3
In Sphere, External Radius R=5cm
Let, Internal Radius = r
Volume of Sphere = External Volume- Internal Volume
= 4/3*pi*R^3-4/3*pi*r^3
=4/3*pi[R^3-r^3]
=4/3*pi[5^3-r^3]
But During Conversion Volume Remains Same
So, Volume of Sphere=Volume of Cone
4/3*pi[125-r^3]= 1/3*pi*49*8
4[125-r^3]=49*8
[125-r^3]=49*2
r^3=125-98
r^3=27
so, r =3 cm
Internal Radius= 3cm
So, Internal Diameter=3*2= 6cm