Question

A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of diameter 0.6 cm. Find the number of small balls thus obtained.
And the difference of surface areas of the solid sphere and the total surface areas the smaller balls. Please!!

Answer 1

Answer:

Given, radius of solid sphere = r = 3cm

Radius of spherical ball = r’ = 0.3 cm

Let n small balls be formed.

So, n × volume of small spherical ball = volume of solid sphere

n × 0.33 = 33

n = 103

n = 1000.

Step-by-step explanation:

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Answer 2

Number of spherical balls is 1000 and the difference of surface areas of the solid sphere and the total surface areas the smaller balls is 324 cm²

Step-by-step explanation:

Given : Radius of large sphere r = 3 cm

            Diameter of Small spherical balls = 0.6 cm

Therefore

Radius of small spherical calls r' = 0.3 cm

Now we have to find the number of smaller balls that can be made from Large sphere

As we recast after melting the volume remains same

$n=\dfrac{\text {Volume of large sphere}}{\text {Volume of small spherical balls}}$

where n is the number of spherical balls

Now as we know Volume of sphere is given by $\dfrac{4}{3} \pi r^3$

therefore

$n=\dfrac{\dfrac{4}{3} \pi r^3 }{\dfrac{4}{3} \pi r'^3} \\\\\Rightarrow n =\dfrac{r^3}{r'^3} \\\\\Rightarrow n=\dfrac{3 \times 3\times 3}{0.3 \times 0.3\times 0.3} =1000$

Hence 1000 spherical balls can be made after recasting

Surface area of solid sphere = $4 \pi r^2 = 4 \times\pi \times 3\times 3 = 36\pi cm^2$

Surface area of 1 spherical ball= $4 \pi r^2 = 4 \times\pi \times 0.3\times 0.3 = 0.36\pi cm^2$

Surface area of 1000 spherical balls = 0.36 x 1000 = 360 cm²

Hence, the difference of surface areas of the solid sphere and the total surface areas the smaller balls =360 - 36 = 324 cm²

#Learn more

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