Question

1)The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller
spheres of diameter 3.5 cm. How many such spheres can be obtained?

2)The surface area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid
right circular cones of radius 2.5 cm and height 8 cm. Calculate:
(i) the radius of the solid sphere.
(ii) the number of cones recast. (Use π= 3.14).​

Answer 1

Answer:Hope this is help full

Step-by-step explanation:

Solution:-

Surface area of the sphere = 4πr²

616 = 4*22/7*r²

r² = (616*7)/88

r² = 4312/88

r² = 49 

r = 7 cm

Radius of the sphere is 7 cm

As sphere is melted and recast into a cone then,

Volume of the sphere = Volume of the cone

4/3πr³ = 1/3πr²h

4/3*22/7*7*7 = 1/3*22/7*r²*28

4/3*7*7*7 = 1/3*r²*28

r² = 49

r = 7 cm

So, radius of the cone is 7 cm and diameter = 7*2 = 14 cm

Answer.