Radius of hemispherical bowl = 9 cm \[Volume\text{ }=\text{ }2/3\text{ }\pi {{r}^{3}}~=\text{ }2/3\text{ }\pi {{9}^{3}}~=\text{ }2/3\text{ }\pi \text{ }x\text{ }729\text{ }=\text{ }486\text{ }\pi...

### A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.

Volume of rectangular block \[=\text{ }49\text{ x }44\text{ x }18\text{ }c{{m}^{3}}~=\text{ }38808\text{ }c{{m}^{3}}~\ldots \ldots \text{ }\left( i \right)\] Let r be the radius of sphere....

### Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.

Let the radius of the smaller cone be r cm Diameter of bigger cone = 40 cm the radius = 20 cm and height = 9 cm \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }larger\text{ }cone\text{ }=\text{...

### The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. find the diameter of the base of the cone.

Height of the solid right circular cone = 32 cm Internal radius metallic spherical shell = 3 cm External radius spherical shell = 5 cm the volume of the spherical shell \[\begin{array}{*{35}{l}}...

### A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.

External diameter of the hollow sphere = 8 cm radius (R) = 4 cm Internal diameter of the hollow sphere = 4 cm radius (r) = 2 cm Then, the volume of metal used in hollow sphere = Also given, Diameter...

### A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.

Radius of the sphere = R = 15 cm So, the volume of sphere melted \[=\text{ }4/3\text{ }\pi {{R}^{2}}~=\text{ }4/3\text{ x }\pi \text{ x }15\text{ x }15\text{ x }15\] Radius of each cone recasted = r...