Surface Area and Volume

Conversion of one solid into another solid

Some time we have to melt one solid and convert it to another shap. For example we have to convert a metallic sphere to wire in the form of cylinder. The earth taken out from a well and is spreed around to make embankment of the form of cylindrical shell.

Example 1. A rectangular sheet of paper 44cm X 18cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder.

Solution:-

Let height, h of the cylinder be 18cm

Circumference of the base

Now,

Volume of the cylinder =

Example 2. How many metres of cloth 1.1m wide will be required to make a conical tent whose vertical height is 12cm and base radius is 16m? Find also the cost of the cloth used at the rate of Rs. 14 per metre.

Solution:- Radius, r of base of conical tent = 16m.

Height, h of tent = 12m

Slant height l =

Curved surface area of the tent

Area of cloth = 7040/7 m²

Width of the cloth = 1.1m

Lenght of the cloth = Area/width

Cost of 6400/7m cloth = Rs. 14 X 6400/7 = Rs. 12800.