Question

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

Answer 1

Answer:

6 cm

Step-by-step explanation:

volume of cone is, 1/3πr²h

volume of sphere is 4/3π r³

since the child reshapes the cone into a sphere, the volume of sphere and cone will be equal. thus,

1/3r²πh = 4/3πr³

h=4r

thus, r= h/4

r= 24/4 = 6cm

Answer 2

Given :-

Height of the cone = 24 cm

Radius of the cone = 6 cm

A child reshapes it in the form of a sphere.

To Find :-

The radius of the sphere.

Solution :-

We know that,

• h = Height
• d = Diameter
• r = Radius

By the formula,

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

Given that,

Height of the cone = 24 cm

Radius of the cone = 6 cm

Substituting their values,

$\sf =\dfrac{1}{3} \pi \times (6)^{2} \times 24$

$\sf =\dfrac{1}{3} \pi \times 36 \times 24$

$\sf =288 \pi \ cm^{3}$

Therefore, the volume of cone is 288π cm³

Next,

Let the radius of the sphere be 'r'.

By the formula,

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

Given that,

Volume of sphere = Volume of cone

By substituting,

$\sf \dfrac{4}{3} \pi r^{3}=288\pi$

$\sf \dfrac{4}{3} r^{3}=288$

$\sf r^{3}=\dfrac{288 \times 3}{4}$

$\sf r^{3}=72 \times 3$

$\sf r^{2}=8 \times 9 \times 3$

$\sf r^{3}=( 2\times 2 \times 2 \times 3 \times 3 \times 3)$

$\sf r=( 2\times 2 \times 2 \times 3 \times 3 \times 3)^{\frac{1}{3} }$

$\sf r=(2^3)^{\frac{1}{3} }\times (3^{3})^{\frac{1}{3} }$

$\sf r=2 \times 3$

$\sf r=6$

Therefore, the radius of the sphere is 6 cm.