Question

What is the radius of the circular plate of thickness 1cm made by melting a sphere of radius 3cm?

a. 6 cm

b. 5 cm

c. 4 cm

d.7 cm?

Answer 1

Given that radius of sphere r=3 cm

Given that thickness of the plate h=1 cm

Given that a sphere is melt to produce a circular plate.

Since nothing is added or subtraced then volume of sphere and circular plate both will be equal.

Volume of sphere $= \frac{4}{3}\pi\ r^3 = \frac{4}{3}\pi\ *3^3$

Volume of circular plate$= \pi r^2h = \pi r^2*1$

set both volumes equal to each other

$\frac{4}{3}\pi\ *3^3 = \pi r^2*1$

$\frac{4}{3}\pi\ *27=\pi r^2$

$4\pi\ *9=\pi r^2$

$4*9=r^2$

$36=r^2$

6=r

Hence final answer is 6 cm.