A sphere is melted to make six cylinder has a diameter 4cm,height 12cm and what is the radius?
Answers
Step-by-step explanation:
Diameter of cylinder (d) = 4cm (given)
So, Radius of cylinder (r) = d/2
= 2cm
Height of cylinder (h) = 12cm (given)
Volume of 1 cylinder = πr^2h
= 22/7 × (2)^2 × 12
= 22/7 × 4 × 12
= 1056/7 cm^3
Given, a sphere is melted to form 6 such cylinders.
Therefore, Volume of sphere = Volume of 1 cylinder × 6
=> 4/3 πR^3 = 1056/7 × 6
=> 4/3 πR^3 = 6336/7
=> πR^3 = 6336/7 ÷ 4/3
=> 22/7 × R^3 = 6336/7 × 3/4
=> R^3 = 4752/7 ÷ 22/7
=> R^3 = 4752/7 × 7/22
=> R^3 = 216
Therefore, R = 3^√216
= 6cm
So, Radius of the sphere (R) = 6cm.
Hope it helps :)
Answer :
- Radius of the sphere (R) = 6cm.
Given :
- A sphere is melted to make six cylinder.
- Diameter = 4cm
- Height = 12 cm
To find :
- The radius = ?
Step-by-step explanation :
Diameter of cylinder (d) = 4cm (given)
∴ Radius (r) = d/2
= 2cm
Height of cylinder (h) = 12cm (given)
Volume of cylinder = πr^2h
Substituting the values in the above formula, we get :
= 22/7 × (2)³ × 12
= 22/7 × 4 × 12
= 1056/7 cm³
Now,
Volume of sphere = Volume of 1 cylinder × 6
Substituting the values in the above formula, we get :
4/3 πR³ = 1056/7 × 6
4/3 πR³ = 6336/7
πR³ = 6336/7 ÷ 4/3
22/7 × R³ = 6336/7 × 3/4
R³ = 4752/7 ÷ 22/7
R³ = 4752/7 × 7/22
R³ = 216
R = ³√216
R = 6cm