The volume of first sphere = 27 x volume of second sphere Let the radius of the first sphere = r1 and, radius of second sphere = r2 (i) Then, according to the question we have...

### 8 metallic sphere; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.

Radius of metallic sphere = 2mm = 1/5 cm \[\begin{array}{*{35}{l}} Volume\text{ }=\text{ }4/3\text{ }\pi {{r}^{3}}~=\text{ }4/3\text{ x }22/7\text{ x }1/5\text{ x }1/5\text{ x }1/5\text{ }=\text{...

### How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm.

Diameter of bigger ball = 8 cm radius of bigger ball = 4 cm \[Volume\text{ }=\text{ }4/3\text{ }\pi {{r}^{3}}~=\text{ }4/3\text{ }\pi \text{ }{{4}^{3}}~=\text{ }265\pi /3\text{ }c{{m}^{3}}\] Radius...

### A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?

Let the radius of the spherical ball = r the volume = 4/3 πr3 And, the radius of smaller ball = r/2 Volume of smaller ball \[=\text{ }4/3\text{ }\pi {{\left( r/2 \right)}^{3}}~=\text{ }4/3\text{...

### The volume of a sphere is 38808 cm3; find its diameter and the surface area.

Volume of the sphere = 38808 cm3 Let the radius of the sphere \[\begin{array}{*{35}{l}} =\text{ }r \\ 4/3\text{ }\pi {{r}^{3}}~=\text{ }38808 \\ 4/3\text{ x }\left( 22/7 \right)\text{ x...

### The surface area of a sphere is 2464 cm2, find its volume.

Surface area of the sphere = 2464 cm2 Let the radius of the sphere be r. surface area of the sphere \[\begin{array}{*{35}{l}} =\text{ }4\pi {{r}^{2}} \\ 4\pi {{r}^{2}}~=\text{ }2464 \\ 4\text{ x...