Math, asked by uma9642, 11 months ago

A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.​

Answers

Answered by Anonymous
30

⠀⠀ıllıllı uoᴉʇnloS ıllıllı

\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}

The volume of cone = (⅓) × π × 6 × 6 × 24 cm³

If r is the radius of the sphere, then its volume is (4/3) πr³.

Since the volume of clay in the form of the cone and the sphere remains the same,

We have:

➠ (4/3) πr³ = (⅓) × π × 6 × 6 × 24 cm³

➠ r³ = 3 × 3 × 24 = 3³ × 2³

➠ So, r = 3 × 2 = 6

  • Therefore, the radius of the sphere is 6 cm.

\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}

Answered by pandaXop
3

Radius of Sphere = 6 cm

Step-by-step explanation:

Given:

  • Height of cone is 24 cm.
  • Radius of base of cone is 6 cm.
  • Cone is reshaped into sphere.

To Find:

  • What is the measure of radius of sphere?

Solution: As we know that Volume of cone is

Volume of cone = ( 1/3πr²h ) cubic units

\implies{\rm } 1/3 \times π \times (6)² \times 24 cm³

\implies{\rm } 1/3 \times π \times 36 \times 24 cm³

\implies{\rm } 288π cm³

If 'r' the radius of the sphere , then volume of sphere is :-

Volume of sphere = ( 4/3πr³ ) cubic units

\implies{\rm } 4/3 \times π \times cm³

Since, the volume of clay in the form of cone and the sphere remains the same, therefore both volumes will be equal i.e

  • Volume of cone = Volume of sphere

\implies{\rm } 288π = 4/3 \times π \times r³

\implies{\rm } 288 = 4/3 \times

\implies{\rm } 288 \times 3 = 4 \times r³

\implies{\rm } 864 = 4 \times

\implies{\rm } 864/4 =

\implies{\rm } 216 =

\implies{\rm } ³6 \times 6 \times 6 = r

\implies{\rm } 6 cm = r

Hence, the radius of sphere is 6 cm.

_______________________

Other Formulae ★

➭ CSA of cone = πrl

➭ TSA of right circular cone = πr(l + r )

➭ Surface area of sphere = 4πr²

Attachments:
Similar questions