Question

A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is
(a)2r
(b)3r
(c)r
(d)4r

Answer 1

Answer:

The Radius of the base of the cone is 2r.

Among the given options option (a) 2r is the correct answer.

Step-by-step explanation:

Given :  

A solid sphere of radius =  r  

solid cone of height,h =  r

Let the radius of the cone be ‘R’  

Volume of sphere =  Volume of cone

[Sphere is melted and recast in the shape of cone]

4/3 πr³ =  ⅓ πR²h

4r³ = R²(r)

4r³/r = R²

4r² = R²

R = √(4r²)

R = 2r

Radius of the cone = 2r

Hence, the Radius of the cone is 2r.

HOPE THIS ANSWER WILL HELP YOU…..

Answer 2

$\mathfrak\pink{Question}$

A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is

(a)2r

(b)3r

(c)r

(d)4r

$\mathfrak\red{Answer}$

$\bold{We, \: know \:that}$

$\bold{Volume\:of\: sphere} = \bold{\frac{4}{3} \pi \: r {}^{3}}$

$\bold{Volume\:of\: cone} = \bold{ \frac{1}{3} \pi \: r {}^{2}h }$

Now,

$\mathfrak\red{Let\:the \:radius\:of \:the\:base=x}$

$→ \bold{\frac{4}{3} \pi \: r {}^{3}} = \bold{ \frac{1}{3}\pi \times x {}^{2} \times r } \:$

$→\bold{x = 2r}$

Therefore,

$\mathfrak\orange{Option \:A\:is \:the\:Answer}$