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 $(\pi=\frac{22}{7})$).

Answer 1

Answer:

The diameter of the base of the cone is 14 cm

Step-by-step explanation:

Given :  

Let R be the radius of the cone

Surface area of the Solid metallic sphere = 616 cm²  

Height of the cone , h = 28 cm

Surface area of the sphere = 4πr²

616 =  4 × 22/7 × r²

616 × 7 = 88r²

r² = (616 × 7)/88

r² = 7 × 7  

r = √7 × 7

r = 7

Radius of the sphere = 7 cm

Volume of the Solid metallic sphere =  4/3πr³

Volume of the cone = 1/3πr²h

Since, the Solid metallic sphere is melted and recast into a cone , so volume of both are equal

Volume of the Solid metallic sphere = Volume of the cone  

4/3πr³ = 1/3πR²h

4r³ = R²h

4 × 7³ = R² × 28

R² = (4 × 7 × 7 × 7) / 28

R² = 7 × 7

R = √7 × 7

R = 7 cm

Radius of the cone, R = 7 cm

Diameter of the cone = 2 × R = 7 × 2 = 14 cm

Hence, the diameter of the base of the cone is 14 cm.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Step by step explanation :

We know that,

Total Surface Area of sphere = 4πr^2

4 ×22/7 ×r^2 = 616

r^2 = 616 × 1/4 ×7/22

r^2 = 49

r = radius of sphere = 7 cm.

Now,

Volume of sphere = Volume of cone

4/3 × π r^3 = 1/3 × π R^2 × h

4/3 × 7 × 7 × 7 = 1/3 × R^2 ×28

R^2 = 49

R = 7

Diameter of base of the cone = 2 × R

= 2 × 7

= 14cm

Thus, the diameter of the base of the cone so formed is 14 cm.