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

Given:-

• Diameter of Cylinder is 2 cm and Height is 16 cm.

• Total sphere formed is 12.

To Find:-

• Diameter of the each sphere ?

Solution:-

Here, T.S.A of Cylinder is πr²h

And, T.S.A of Sphere is $\dfrac{4}{3}$πr³

∵ Radius of the Cylinder ⇒ $\dfrac{Diameter}{2}$

                                        ⇒ $\dfrac{2cm}{2}$          ⇔ 1 cm

Now, Volume of Cylinder ⇒ πr²h

                                          ⇒ π × 1² × 16

                                          ⇒ 16π cm³

So, Volume of Spheres ⇒ 12 × $\dfrac{4}{3}$πr³

                 16π cm³ ⇒ 12 × $\dfrac{4}{3}$ × π × r³

                    $\dfrac{16\pi cm^{3}}{\pi}$  ⇒ 16 × r³

                             r³ ⇒ $\dfrac{16}{16}$ cm³

                               r ⇒ ∛1 cm³

                               r ⇒ 1 cm

Hence, Diameter of a Sphere ⇒ 2 × 1 cm ⇔ 2 cm

Some Important Terms:-

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\end{array}$