Question

The surface area of a solid metallic sphere is 616 cm². It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed.Use $\pi = \frac{22}{7}$
OR
The difference between the outer and inner curved surface areas of a hollow right circular cylinder, 14 cm long, is 88 cm. If the volume of metal used in making the cylinder is 176 cm , find the outer and inner diameters of the cylinder. Use $\pi = \frac{22}{7}$

Answer 1

1.

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.