Question

1. 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

Given:

The government has the 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.

To find:

When the machine operator dug out the field in the given dimension, the three-dimensional shape of the digging area is?

Find the volume of the soil?

How much cover area of the field dug out?

Find the total inner surface area of the digging field?

If the cost of digging out of 1 cubic metre field is Rs 50, find the total cost of complete digging out the field.

Solution:

Finding the shape of the digging area:

When the machine operator dug out the field in the given dimension, the three-dimensional shape of the digging area is → cylindrical-shaped

Finding the volume of the soil:

The radius of the circular-shaped cut-out = 3 m

The depth = 10 m

∴ The volume of the soil is,

= Volume of the earth dug-out of the field in the shape of a cylinder

= $\pi r^2 h$

= $\frac{22}{7} \times 3^2 \times 10$

= $\boxed{\bold{282.85 \:m^3 }}$

Finding the cover area of the field dug out:

Since the cover of the dug-out portion of the field is circular shape

∴ The cover area of the field dug-out is,

= Area of a circle

= $\pi r^2$

= $\frac{22}{7} \times 3^2$

= $\boxed{\bold{28.28 \:m^2}}$

Finding the total inner surface area of the digging field:

The total inner surface area of the digging field is,

= Total Surface Area of a cylinder

= $2\pi r(r + h)$

= $2\times \frac{22}{7} \times 3 \times (3 + 10)$

= $2\times \frac{22}{7} \times 3 \times 13$

= $\boxed{\bold{245.14 \: m^2}}$

Finding the total cost of complete digging out the field:

If the cost of digging out 1 m³ of the field = Rs. 50

Then,

The cost of digging out 282.85 m³ of the field = 50 × 282.85 = Rs. 14142.50

Thus, the total cost of complete digging out the field is Rs. 14142.50.

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