A hemispherical bowl of internal and external diameters 6 cm and 10 cm is melted and formed into a cylinder of diameter 14 cm. Find the height of the cylinder.
Answers
___Heya Mate Your solution is..!!
If any solid particle is melted and formed new particle by it then
volume of first particle=volume of 2nd particle
now,
volume of bowl=2/3π{R^3-r^3}
where R is external
and
r is internal radius of bowl
volume of bowl =2/3 π{(5)^3-(3)^3}=2/3 x πx{125-27}=2/3 x π x 98=196/3π cm^3
let length of cylinder =h
volume of cylinder=πR1^2.h=π(7)^2h
now,
49π.h=196π/3h=4/3 cm
_____HOpe iT HelP YOu DEaR
Question :--- A hemispherical bowl of internal and external diameters 6 cm and 10 cm is melted and formed into a cylinder of diameter 14 cm. Find the height of the cylinder ?
Concept and Formula used :--
→ when any solid object is melted and recast into another object, than their volume will remain same..
→ Volume of Hollow Hemisphere = 2/3 * π * [ R³ - r³ ]
→ Volume of Cylinder = π * r² * h
_____________________________
Solution :---
Given,
→ External Diameter of Hemisphere = 10cm
→ so, External Radius = R = 10/2 = 5cm.
→ Internal Diameter = 6cm.
→ so, internal Radius = 6/2 = 3cm.
→ Diameter of Cylinder = 14cm .
→ So, Radius of cylinder = 14/2 = 7cm.
Now, Let Height of cylinder is = H cm.
Since , volume of both will be same.
So, putting all values we get,
→ 2/3 * π * (5³ - 3³) = π * 7² * H
π will cancel From both sides ,
→ 2 * ( 125 - 27) = 49 * 3 * H
→ 2 * 98 = 147 * H
→ 196 = 147 * H
→ H = 196/147
→ H = 1.33 cm.