Question

The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of height 2 2/3 cm. Find the diameter of the cylinder.

Answer 1

Diameter of the cylinder is 14 cm.

To find : The diameter of the cylinder.

Given :

Radius ( $r_1$ ) of the internal surface of a hollow spherical shell = 3 cm.

Radius ( $r_2$ )of the external surface of a hollow spherical shell = 5 cm.

Cylinder height = $2\frac{2}{3}$ cm = $\frac{8}{3}$ cm.

Let the cylinder radius be $r_3$.

Formula used :

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

Volume of cylinder = $\pi r^2h$

Hence, sphere has two radius $r_1$ and $r_2$.

So, r = $r_2 - r_1$

Volume of sphere = Volume of cylinder

$\frac{4}{3}\pi (r_2^3- r_1^3) = \pi r_3^2h$

Here, "$\pi$" get cancel each other.

$\frac{4}{3}(r_2^3 - r_1^3) =r_3^2h$

Substituting the values of radius and height, we get

$\frac{4}{3} ((5)^3 - (3)^3) = r_3^2\times \frac{8}{3}$

$\frac{4}{3} (125 - 27) = r_3^2\times \frac{8}{3}$

$\frac{4}{3} (98) = r_3^2\times \frac{8}{3}$

$\frac{4 \times 98 \times 3}{3 \times 8}=r_3^2$

$r_3^2 =$ $\frac{4 \times 98}{8}$

$r_3^2= \frac{98}{2}$

$r_3^2= 49$

$r_3= \sqrt{49}$

$r_3=7$

Hence, the radius of the cylinder is 7 cm.

Diameter of the cylinder = 2 × radius = 2 × $r_3$ = 2 × 7 = 14 cm.

Therefore, the diameter of the cylinder is 14 cm.

To learn more...

1. The radii of internal and external surfaces of a hollow spherical shell at 3 cm and 5 cm respectively it is melted and recast into a solid cylinder of diameter 14 cm find the height of the cylinder

brainly.in/question/7851326

2. The internal and external radii of a hollow spherical shell are 3 cm and 5cm respectively. if it is melted and recast into a solid cylinder of diameter 14 cm . find the heigt of the cylinder

brainly.in/question/7224093

Answer 2

$\underline\mathfrak{Given:-}$

• The radius of the internal and external of a hollow of a hollow spherical shell are 3cm and 5cm.
• A solid cylinder of height 2 2/3 cm.

$\underline\mathfrak{To \: \: Find:-}$

• Find the the diameter of the cylinder ......?

$\underline\mathfrak{Solutions:-}$

Radius of the internal surface of a hollow spherical shell = 3cm.

Volume of sphere in internal shell

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \pi \: {r}^{3}$

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \times \: \pi \: \times \: {(3)}^{3}$

Radius of the external surface of a hollow spherical shell = 5cm.

Volume of sphere in external shell

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \pi \: {r}^{3}$

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \times \: \pi \: \times \: {(5)}^{3}$

Volume of metal

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \pi \: \times \: {(5)}^{3} \: - \: \frac{4}{3} \: \times \: \pi \: \times \: {(3)}^{3}$

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \pi \: {({(5)}^{3} \: - \: {(3)}^{3})}$

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \pi \: {({125} \: - \: {27})}$

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \pi \: {({125} \: - \: {27})}$

$\: \: \: \: \: \leadsto \: \: \frac{4}{3} \: \pi \: \times \: {98} \: {cm}^{3}$

height of cylinder = 8/3 cm

$\: \: Volume \: \: of \: \: cylinder \: \: \leadsto \: \: \frac{4}{3} \: \pi \: \times \: {98} \: {cm}^{3}$

$\: \: \: \: \: \leadsto \: \: \pi \: {r}^{2} \: h \: \: = \: \: \frac{4}{3} \: \pi \: \times \: {98}$

$\: \: \: \: \: \leadsto \: \: {r}^{2} \: \: = \: \: \frac{4}{3} \: \times \: {98} \: \times \: \frac{3}{8}$

$\: \: \: \: \: \leadsto \: \: {r}^{2} \: \: = \: \: {49}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: {7}$

Diameter of cylinder

= 2 × 7

= 14cm

Hence, the diameter of cylinder is 14cm.