Question

A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is
(a)4 cm
(b)5 cm
(c)6 cm
(d)8 cm

Answer 1

Answer:

The radius of a cone is 8 cm.

Among the given options option (d) 8 cm  is the correct answer.

Step-by-step explanation:

Given :  

Radius of a cylinder ,R = 8 cm

Height of a cylinder, h = 2 cm  

Height of a cone ,H = 6 cm

 

Let r the radius of a cone

 

Volume of the cylinder = volume of cone

[Cylinder is melted to form a cone]

πR²h = 1/3 πr²H

R²h = 1/3 r²H

8² × 2 = ⅓ × r² × 6

64 × 2 = 2r²

r² = (64 × 2)/2

r² = 64

r = √64

r = 8 cm

Radius of a cone = 8 cm

Hence, the radius of a cone is 8 cm.

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Answer 2

Radius of the cylinder = 8 cm

Height of the cylinder = 2 cm

Height of the cylinder = 6 cm

Given : Cylinder is melted to form a cone

That means, Volume of the cylinder = Volume of the cone

πR²h = ⅓ πr²h

8² * 2 = ⅓ * r² * 6

64 * 2 = ⅓ * r² * 6

128 = ⅓ * r² * 6

(128 * 3)/6 = r²

384/6 = r²

64 = r²

r = √64

r = 8

Therefore the radius of the cone is option (d) 8 cm.