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Home » 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).
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).
CBSE | Class 10 | Exercise 1 | maths | Maths | Mensuration | ML Aggarwal
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).

Solution:

(i)Given surface area of the solid metallic sphere = 1256 cm2

4R2 = 1256

4×3.14×R2 = 1256

R2 = 1256/4×3.14

R2 = 100

R = 10

Hence the radius of solid sphere is 10 cm.

(ii)Volume of the solid sphere = (4/3)R3

= (4/3)×103

= (4000/3) cm3

= 12560/3 cm3

Radius of the cone, r = 2.5 cm

Height of the cone, h = 8 cm

Volume of the cone = (1/3)r2h

= (1/3)×3.14×2.52×8

= 157/3 cm3

Number of cones made = Volume of the solid sphere/ Volume of the cone

= (12560/3)÷( 157/3)

= (12560/3)×( 3/157)

= 12560/157

= 80

Hence the number of cones made is 80.

i

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