Question

Three solid spheres of diameter 2cm, 12cm and 16cm are melted and made into single sphere. Find the radius of the new sphere​

Answer 1

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Step-by-step explanation:

GIVEN -

DIAMETER OF 1ST SPHERE=2CM

DIAMETER OF 2ND SPHERE=12CM

DIAMETER OF 3RD SPHERE=16CM

MYSTERY TOPIC-

WHAT IS THE RADIUS OF THE FINAL MADE SPHERE????

Formula-

$\frac{4}{3} \pi \times {r}^{3} = volume \: of \: sphere$

We will have to find the volumes of all the spheres and add them.

volume of 1st sphere-

$\frac{4}{3} \pi \times {1}^{3}$

note - we have made the diameters half to get radius.

$= \frac{4}{3} \pi$

volume of 2nd sphere-

$\frac{4}{3} \pi \times {6}^{3}$

$\frac{864}{3} \pi$

volume of 3rd sphere-

$\frac{4}{3} \pi \times {8}^{3}$

$= \frac{2048}{3} \pi$

now find the sum....

$\frac{4}{3} \pi + \frac{864}{3} \pi + \frac{2048}{3} \pi$

$\frac{\pi}{3} (4 + 864 + 2048)$

$\frac{\pi}{3} \times 2916$

$= 3054.857 {cm}^{3}$

now this is the volume of the last made sphere so we can find out the radius-

$3054.857 = \frac{4}{3} \pi \times {r}^{3}$

$3054.857 \div \frac{88}{21} = {r}^{3}$

$12801.2764 = {r}^{3}$

$\sqrt[3]{12801.2764} = r$

$113.01 = r$

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