Answer to Question #151330 in Geometry for Chitransh Kashyap

Question

The government has policy to make a highway as soon as possible. So, the constructor used the heavy machine instead of using man labour. A machine operator dug out a field in the shape of circular having radius 3 m and some depth 10 m. answer the following question.
A. When the machine operator dug out the field in the given dimension , the three dimensional shape of the digging area is ?
B. Find the volume of the soil .
C. How much cover area of the field dug out ?
D. Find the total inner surface area of the digging field.
E. If the cost of digging out of 1 cubic metre field is Rs 50 . find the total cost of complete digging out field.

Answer 1

A. Cylinder

B. Volume of a cylinder =$\pi r^2h\\$

$=\frac{22}{7}\times 3^2 \times 10\\ =282.8571419m^3\\ \approx 282.857m^3$

C. The cover area of the field dug out is $\pi r^2$. Since the cover is circular.

$=\frac{22}{7} \times 3^2\\ =28.2857m^2\\ \approx 28.29m^2$

D. Total inner surface area $=2\pi r(r+h)\\ =2.\frac{22}{7}.3(3+10)\\ =245.14286m^2\\ \approx 245.14m^2$

E. $1m^3=Rs50\\ 282.857m^3=282.857\times Rs50\\ =Rs14142. 85$