Question

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is
(a)2 cm
(b)3 cm
(c)4 cm
(d)6 cm

Answer 1

$\mathfrak\pink{Question}$

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

(a)2 cm

(b)3 cm

(c)4 cm

(d)6 cm

$\mathfrak\orange{Solution}$

$\bold{Volume\:of\:sphere= Volume\:of\:cone}$

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

$\bold{ \frac{4}{3} \times 3 \times 3 \times 3 = \frac{1}{3}{ \times 6 \times 6 \times h}}$

$\bold{h = \frac{108}{6 \times 6}}$

$\bold{h = 3 \: cm}$

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

Answer 2

Given,

Diameter of the metallic spherical ball = 6cm

Radius of the spherical ball = R = 3cm

Diameter of base of the cone = 12cm

Radius of the cone = r = 6cm

Volume of cone = Volume of sphere

1/3πR^2h = 4/3πr^3

1/3 × π × 6 × 6 × h = 4/3 × π × 3 × 3 × 3

1/3 × π × 36 × h = 4 × π × 3 × 3

12 × h = 36

h = 36/12

h = 3cm

Therefore, the height of the cone is 3cm