Question

if cone of height 24cm and base radius 6 cm is melted and recast into a sphere find the radius of sphere

Answer 1

r1 =6cm
h= 24 cm

vol. of cone = 1/3πr1.r1h

atq
vol. of cone = vol of sphere

so
1/3πr1.r1h=4/3πr2.r2.r2
6.6.24=4.r2.r2.r2
6.6.6=r2.r2.r2
r2=6cm

so radius of sphere = 6 cm

Answer 2

The radius of sphere is 6 cm

Step-by-step explanation:

Height of cone = 24 cm

Radius of cone = 6 cm

Volume of cone = $\frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \times 6^2 \times 24$

We are given that cone of height 24cm and base radius 6 cm is melted and recast into a sphere .

So, Volume of cone = Volume of sphere

$\frac{1}{3} \pi 6^2 \times 24 = \frac{4}{3} \pi r^3$

$6^2 \times 24 = 4 \times r^3$

$\frac{6^2 \times 24 }{4}=r^3$

$216 = r^3$

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

6=r

Hence The radius of sphere is 6 cm

#Learn more:

a cone is 8.4 cm height and the radius of its base is 2.1 cm is melted and recast into a sphere find the radius of a sphere

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