Question

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

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Answer 1

given

height of cone = 24 cm

radius of bas of cone = 6cm

$volume \: of \: cone = \frac{ \pi {r}^{2} h}{3}$

$= \frac{22 \times 6 \times 6 \times 24}{ 7\times 3}$

$= 905.14 {cm}^{3}$

acc to Ques

volume of cone = volume of sphere

$905.14 = \frac{4}{3} \pi {r}^{3}$

$\frac{905.14 \times 3 \times 7}{4 \times 22 } = {r}^{3}$

${r}^{3} = 215.99 = 216$

$r = \sqrt[3]{216}$

r=6cm

Answer 2

Answer:

Radius of the sphere = 6 cm

Step-by-step explanation:

Given:

• Height of cone = 24 cm
• Radius of cone = 6 cm
• Cone is reshaped to form a sphere

To Find:

• Radius of the sphere

Concept:

Here the cone is reshaped to form a sphere. That is the volume of the cone and sphere remains constant. Equating their volumes we get the radius of the sphere.

Solution:

Here we are given a cone of height 24 cm and radius 6 cm.

First we need to find the volume of the cone.

Volume of a cone is given by,

Volume of a cone = 1/3 × π × r² × h

where r = radius of the cone

          h = height of the cone

Substitute the data,

Volume of the cone = 1/3 × π × 6² × 24

Volume of the cone = π × 36 × 8

Volume of the cone = 288 π cm³---------(1)

Hence volume of the cone = 288 π cm³

Now we have to find the volume of the sphere

Volume of a sphere is given by,

Volume of a sphere = 4/3 × π × r³------(2)

where r is the radius of the sphere

By given the LHS of equation 1 and 2 are equal, hence RHS also must be equal.

288 π = 4/3 × π × r³

Cancelling π on both sides,

288 = 4/3 × r³

r³ = 288 × 3/4

r³ = 216

r = ∛216

r = 6

Hence radius of the sphere is 6 cm.