Solution:
Sphere – Radius r1 = 12 cm
Cylinder – Radius r2 = 8 cm
h2 = ?
Volume of cylinder = Volume of sphere melted

∴ Height of the cylinder made = 36 cm.

2. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tanks will rise by 21 cm.

Solution:
In cylinder,
r = 7cm = 0.7m
l = 15 km = 15000 m
In tank
l = 50 m
b = 44 m
h = 0.21 m
Volume of water in tank = lbh
= 50 × 44 × 0.21
= 462 m3

3. A conical flask is full of water. The flask has base radius r units and height h units, the water poured into a cylindrical flask of base radius xr units. Find the height of water in the cylindrical flask.

Solution:
The volume of water poured = The volume of the water in the conical flask.

∴ The height of the water in the cylindrical flask = h3x2 units.

4. A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter.

Solution:
Volume of the hollow sphere made = Volume of the cone melted.

5. Seenu’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank) which is in the shape of a cuboid. The sump has dimensions 2 m × 1.5 m × 1 m. The overhead tank has its radius of 60 cm and height 105 cm. Find the volume of the water left in the sump after the overhead tank has been completely filled with water from the sump which has been full, initially.

Solution:
Volume of water in the sump = lbh
= 2 × 1.5 × l = 200 × 150 × 100 = 3000000 cm3

= 1188000 cm3
∴ The volume of water left in the sump = 3000000 – 1188000
= 1812000 cm3

6. The internal and external diameters of a hollow hemispherical shell is 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, then find the height of the cylinder.

Solution:
D = 10 cm,
R = 5 cm
d = 6 cm,
r = 3 cm

Volume of the cylinder made = Volume of hemisphere melted.

∴ Height of the cylinder made = 1.33 cm.

7. A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5 cm and its height is 32 cm, then find the thickness of the cylinder.

Solution:
Volume of the hollow cylinder made = Volume of the sphere melted.

∴ The thickness = External radius – Internal radius
= 5 – 4 = 1

8. A hemispherical bowl is filled to the brim with juice. The juice is poured into a cylindrical vessel whose radius is 50% more than its height. If the diameter is the same for both the bowl and the cylinder then find the percentage of juice that can be transferred from the bowl into the cylindrical vessel.

Solution:
Diameter of the bowl = Diameter of the cylinder

∴ Both volumes are equal.
∴ 100% of juice that can be transferred from the bowl into the cylindrical vessel.