Question

A solid sphere of radius 5 cm is melted and recast into smaller solid cones, each of radius 2 cm and height 5 cm. The

number of cones so formed is *​

Answer 1

Answer:

Number of cones is 25.

Step-by-step explanation:

Given:-

• A solid sphere of radius 5 cm is melted and recast into smaller solid cones, each of radius 2 can and height 5 cm.

To find:-

• The number of cones.

Solution:-

• Radius of sphere = 5 cm.

Formula used :-

${\boxed{\sf{Volume\:of\: sphere=\dfrac{4}{3}\pi\:r^3}}}$

Then,

Volume of the sphere,

$\to \sf \: \dfrac{4}{3} \pi \times {5}^{3} \: {cm}^{3}$

$\to \sf \: \dfrac{4}{3} \pi \times 125 \: {cm}^{3}$

Formula used :-

${\boxed{\sf{Volume\:of\:cone=\dfrac{1}{3}\pi\:r^2h}}}$

• Radius= 2 cm
• Height = 5 cm

Volume of cone,

$\to \sf \: \dfrac{1}{3} \pi \times {2}^{2} \times 5 \: {cm}^{3}$

$\to \sf \: \dfrac{1}{3} \pi \times 4 \times 5 \: {cm}^{3}$

Now find the number of cones.

$\sf{Number\:of\:cones=\dfrac{Volume\:of\: sphere}{Volume\:of\:cone}}$

$\to\sf{Number\:of\:cones=\dfrac{4/3\times\pi\:125}{1/3\times\pi\times\:4\times\:5}}$

$\to\sf{Number\:of\:cones=\dfrac{4\times\pi\times\:125\times\:3}{3\times\pi\times\:4\times\:3}}$

→ Number of cones = 25

Therefore, the number of cones is 25.

Answer 2

$\bf{\underline{Question:-}}$

• A solid sphere of radius 5 cm is melted and recast into smaller solid cones, each of radius 2 cm and height 5 cm. The number of cones so formed is.

$\bf{\underline{Given:-}}$

• Radius of sphere (r) 5cm
• Radius of cone (R) 2cm
• height of cone 5cm

Let,

• Number of cone be x

$\bf{\underline{Formula:-}}$

$\bf{\underline{\red{† Volume\:of\:Sphere = \frac{4}{3}πr^3}}}$

$\bf{\underline{\red{† Volume\:of\:Cone = \frac{1}{3}πr^2h}}}$

$\bf{\underline{Solution:-}}$

† Volume of sphere = No. of cone × Volume of each cone

$\sf → \large \frac{4}{3}×πr^3 = X × \frac{1}{3}πR^2h$

$\sf → \frac{4}{3}r^3 = X × \frac{1}{3}×R^2h$

$\sf → \frac{4}{3}×(5)^3 = X × \frac{1}{3}×(2)^2×5$

$\sf → 4 × 125 = X × 4 ×5$

$\sf → 500 = 20X$

$\sf \large → \frac{500}{20} = X$

$\sf → 25 = X$

$\bf{\underline{Hence:-}}$

• 25 cone are formed in a solid sphere