A solid cone is 25 cm. high and the radius of its base is 50cm. It is melted and recast into a solid sphere. Determine the surface area of the sphere. (Use = 22/7)
Answers
A solid cone is 25 cm. high and the radius of its base is 50cm. It is melted and recast into a solid sphere. Determine the surface area of the sphere. (Use = 22/7)
Volume of solid sphere = Volume of solid cone
(4 / 3) * π * (r^3) = (1 / 3) * π * (r^2) * h
4r = h
h : r = 4 : 1.
Answer:
Step-by-step explanation:
Given that
The Cone is melted and recast into a Sphere.
Volume of the sphere = Volume of the cone
=> (4/3)πr³ = 1375000/21
=> (4/3)×(22/7)×r³ = 1375000/21
=> (88/21)×r³ = 1375000/21
=> r³ = (1375000/31)×(21/88)
=> r³ = (1375000×21)/(21×88)
=> r³ = 1375000/88
=> r³ = 15625
=> r = 25 cm
♦ Radius of the Sphere = 25 cm
We know that
♦ Surface Area of a sphere is 4πr² sq.units
The Surface Area of the Sphere
=> TSA = 4×(22/7)×(25)² cm²
=> TSA = (4×22×25×25)/7 cm²
=> TSA = 55000/7 cm²
=> TSA = 7857.14 cm² (approximately)
Answer :-
♦ The Surface Area of the Sphere is 7857.14 cm²