Threemetallicspheresofradii6cm.,8cm.and10cm.respectivelyaremelted to f

1.	Threemetallicspheresofradii6cm.,8cm.and10cm.respectivelyaremelted to form a single solid sphere. Find the radius of the resulting sphere.A solid metallic sphere of diameter 28 cm is melted and recast into a number2of smaller cones, each of diameter 45 cm and height 3 cm. Find the numberof cones so formed.2 MARKS PROBLEMS
Answer» Let r1, r2 ,r3 be the radius of the given 3 spheres & R be the radius of a single solid sphere. Given : r1= 6cm, r2= 8cm, r3= 10 cm Volume of first metallic sphere (V1)= 4/3π(r1)³ = 4/3 π (6)³ Volume of second metallic sphere (V2)= 4/3π(r2)³ = 4/3 π (8)³ Volume of third metallic sphere (V3) = 4/3π(r3)³ = 4/3 π (10)³ Volume of single solid sphere(V)= 4/3πR³ A .T.Q Volume of 3 metallic spheres= volume of single solid sphere V1+V2+V3 = V 4/3 π (6)³+ 4/3 π (8)³+4/3 π (10)³= 4/3πR³ 4/3π(6³+8³+10³) = 4/3 πR³ 216+ 512+ 1000 = R³ 1728= R³ (12×12×12) = R³ 12³= R³ R= 12

Threemetallicspheresofradii6cm.,8cm.and10cm.respectivelyaremelted to form a single solid sphere. Find the radius of the resulting sphere.A solid metallic sphere of diameter 28 cm is melted and recast into a number2of smaller cones, each of diameter 45 cm and height 3 cm. Find the numberof cones so formed.2 MARKS PROBLEMS

Answer»

Let r1, r2 ,r3 be the radius of the given 3 spheres & R be the radius of a single solid sphere.

Given :

r1= 6cm, r2= 8cm, r3= 10 cm

Volume of first metallic sphere (V1)= 4/3π(r1)³ = 4/3 π (6)³

Volume of second metallic sphere (V2)= 4/3π(r2)³ = 4/3 π (8)³

Volume of third metallic sphere (V3) = 4/3π(r3)³ = 4/3 π (10)³

Volume of single solid sphere(V)= 4/3πR³

A .T.Q

Volume of 3 metallic spheres= volume of single solid sphere

V1+V2+V3 = V

4/3 π (6)³+ 4/3 π (8)³+4/3 π (10)³= 4/3πR³

4/3π(6³+8³+10³) = 4/3 πR³

216+ 512+ 1000 = R³

1728= R³

(12×12×12) = R³

12³= R³

R= 12