Question

How many cubic metres of earth msut be dugout to sink a well 21 m deep and 6 m diameter? Find the cost of plastering the inner surface of the well at Rs. 9.50 per m².

Answer 1

Cubic meter of Earth dugout = 594 m³

The cost of plastering the inner surface of the well = Rs. 3762

The well is in the form of a cylinder . The radius of the well = r = 6/2 = 3 m

The depth of the well = h = 21 m

Total Volume of the well = πr²h

= 22/7 × 9 × 21

= 594 m³

Curved surface area of the well = 2πrh

= 2 × 22/7 × 3 × 21

= 396 m²

Cost of plastering the inner surface of the well = 396 × 9.5

= Rs. 3762

Answer 2

Answer:

The quantity of earth to be dugout for well is 593.46 cubic meters

The cost of plastering the inner surface of the well is Rs 3758.5

Step-by-step explanation:

Given as :

A well is sink , and earth is dugout

The height of well = h = 21 meters

The diameter of well = d = 6 meters

So, The radius of well = r = $\dfrac{d}{2}$

i.e  radius = $\dfrac{6}{2}$ = 3 m

Now,

The shape of well is cylindrical

So, The quantity of earth to be dugout for well = Volume of cylinder

∵ volume of cylinder = π × radius² × height

Or, volume of cylinder = 3.14 × r² × h

Or, volume of cylinder = 3.14 × ( 3 m)² × 21 m

∴ volume of cylinder = 593.46 m³

So, The quantity of earth to be dugout for well =  593.46 m³

Again , According to question

The cost of plastering the inner surface of the well at Rs. 9.50 per m².

So, The curved surface of well = curved surface of cylinder = 2 × π × radius × height

Or, The curved surface of well = 2 × 3.14 × 3 m × 21 m

∴  The curved surface of well = 395.64 m²

Now,

∵ The cost of plastering 1 sq meter = Rs 9.50

∴ The cost of plastering 395.64 sq meter = Rs 9.50 × 395.64 = Rs 3758.5

i.e The cost of plastering the inner surface of the well = Rs 3758.5

Hence, The quantity of earth to be dugout for well is 593.46 cubic meters

And The cost of plastering the inner surface of the well is Rs 3758.5 Answer