Question

12 solid spheres of the same radii are made by melting a solid metallic

cylinder of base diameter 2cm and height 16cm. Find the diameter of the

each sphere.​

Answer 1

Answer:

12 spheres(equal radii) are made from a cylinder of diameter is 2cm and height is 16cm.

NEED TO FIND:-

Diameter of each sphere

SOLUTION:-

we know that,

we know that,volume of cylinder will equal to 12 times of volume of sphere.

\pi {r}^{2} h = 12 \times \frac{4}{3} \pi {r}^{3}πr2h=12×34πr3

r(cylinder)=1cm

h(cylinder)=16cm

\pi ({1})^{2}(16) = 12 \times \frac{4}{3} \pi {r}^{3}π(1)2(16)=12×34πr3

16 = 4 \times 4 {r}^{3}16=4×4r3

{r}^{3} = \frac{16}{16}r3=1616

{r}^{3} = 1r3=1

r = \sqrt[3]{1}r=31

r = 1r=1

diameter=2r

=2×1

=2cm

Answer 2

Diameter of each sphere will be 2 cm