Question

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones is
(a)63
(b)126
(c)21
(d)130

Answer 1

Answer:

The number of such cones is 126.

Among the given options option (b) 126 is the correct answer.

Step-by-step explanation:

Given :  

Radius of a metallic sphere , R = 10.5 cm

Radius of a cone , r = 3.5 cm  

Height of a cone , h = 3 cm

Let ‘n’ be the number of cones.

Volume of metallic sphere = n × Volume of cone

n = Volume of metallic sphere / Volume of cone

n = 4/3 πR³ /  ⅓ πr²h

n = 4R³ / r²h

n = 4 × (10.5)³ / 3.5² × 3  

n = (4 × 10.5  × 10.5 × 10.5) / (3.5 × 3.5  × 3)  

n = (4 × 3 × 3 × 3.5)

n = 36 × 3.5

n = 126  

Number of cones = 126  

Hence, the number of cones is 126.

HOPE THIS ANSWER WILL HELP YOU…..

Answer 2

$\mathfrak\pink{Question}$

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones is

(a)63

(b)126

(c)21

(d)130

$\mathfrak\orange{Solution}$

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

$= \frac{4}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5$

$= 4851 \: cm {}^{3}$

$\mathfrak\red{Now, \:we \:have\: to\: find\: the\: volume \:of \:cone}$

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

$= \frac{1}{3} \times \frac{22}{7} \times 3.5 \times 3.5 \times 3$

$= 38.5 \: cm {}^{3}$

${Number\: of\: cones}= \frac{\bold{volume\: of\: sphere}}{\bold{volume\: of\: cone}}$

$= \frac{4851}{38.5}$

$\bold\red{126 \:cones}$ is the answer

Therefore,

$\mathfrak\purple{Option\:B \:is \:the\:answer}$