Math, asked by lucky16022006, 8 months ago

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 *​

Answers

Answered by Anonymous
22

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.

Answered by Anonymous
13

\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
Similar questions