Question

By melting down a sphere of radius 10.5 CM some small cones are made each of height 3 cm and radius 3.5 cm find the number of such cones​

Answer 1

$Given \: that$

$Metallic \: sphere \: of \: radius = 10.5cm$

$Cone \: radius = 3.5cm$

$Let \: the \: number \: of \: cones \: be \: X$

$V = x \times V \: cone$

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

$\frac{4 \times 10.5 \times 10.5 \times 10.5}{3.5 \times 3.5 \times 3} = x$

$x = 126$

$∴Number \: of \: cones = 126$

Answer 2

Answer:

⟾ 126.

Step-by-step explanation:

Radius of sphere r = 10.5 cm

Radius of cone r = 3.5 cm

Height of cone r = 3 cm

$∴ \: \: \: volume \: of \: sphere \: = \frac{4}{3} \pi \: {r}^{3}$

$⇉ \frac{4}{3} \pi(10.5 {)}^{3}$

$volume \: of \: cone \: = \frac{1}{ 3} \pi \: {r}^{3} h$

$⇉ \frac{1}{3} \pi(3.5 {)}^{2} \times 3$

$⇉ \pi \times (3.5 {)}^{2}$

Let n cones are made by melting the sphere.

Then,Volume of n cones = Volume of sphere

$➠n \times \pi.(3.5 {)}^{2} = \frac{4}{3} \pi(10.5 {)}^{3}$

$➠ \: \: n = \frac{ \frac{4}{3} \times (10.5 {)}^{3} }{(3.5 {)}^{2} }$

$\: \: \: \: \: = \frac{4 \times 10.5 \times 10.5 \times 10.5}{3 \times 3.5 \times 3.5}$

$\: \: \: = \frac{4 \times 3.5 \times 10.5 \times 10.5}{3.5 \times 3.5}$

$\: \: \: \: = \frac{4 \times 1.5 \times 10.5}{0.5}$

$\: \: \: \: \: = 4 \times 3 \times 10.5$

$\: \: \: \: = 126.$