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Basic Civil Engineering

S S Bhavikatti

Chapter 18

Areas and Volumes - all with Video Answers

Educators


Chapter Questions

03:41

Problem 1

Find the area of the field from the following notes of cross staff survey, all measurements being in metres.

Shuyang Fu
Shuyang Fu
Numerade Educator
01:26

Problem 2

The following obeervatione were taken to a boundary from a chain line.
$$
\begin{array}{lllllllll}
\text { Distance in } \mathrm{m} & 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70 \\
\text { Offset in } \mathrm{m} & 2.4 & 3.6 & 4.2 & 4.8 & 4.4 & 3.8 & 2.8 & 1.2
\end{array}
$$

Calculate the area enclosed between the chains line, the boundary line and the end offsets by
(i) Trapezoidal rule
(ii) Simpson's rule

Dharmendra Jain
Dharmendra Jain
Numerade Educator
01:58

Problem 3

A plot of ground is in the form of a quadrilateral. To find the area the following measurements were taken:

$$
\begin{aligned}
& \mathrm{AB}=118.6 \mathrm{~m} \quad \mathrm{BC}=220.4 \mathrm{~m} \quad \mathrm{CD}=158.4 \mathrm{~m} \\
& \mathrm{DA}=340.0 \mathrm{~m} \text { and } \mathrm{AC}=322.0 \mathrm{~m}
\end{aligned}
$$

Find the area of the plot.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator

Problem 4

Describe the planimeter and explain how it is used for finding the area of a given map.

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02:30

Problem 5

A planimeter was used to measure the area of a map once keeping anchor point outside the figure and second time keeping it inside the figure. The observations are as follows:
(i) When anchor point was outside the figure:

$$
\begin{aligned}
\text { Initial reading } & =7.364 \\
\text { Final reading } & =3.234
\end{aligned}
$$

The zero of dial passed the index mark once in the clockwise direction.
(ii) When anchor point was inside the figure:

$$
\begin{aligned}
\text { Initial reading } & =2.384 \\
\text { Final reading } & =4.443
\end{aligned}
$$

The zero of the dial passed the index mark twice in the anticlockwise direction. Take $\mathrm{M}=100 \mathrm{~cm}^2$.

Arpit Gupta
Arpit Gupta
Numerade Educator
01:40

Problem 6

How do you determine the multiplying constant and area of zero circle of a planimeter experimentally ?

Manik Pulyani
Manik Pulyani
Numerade Educator
04:37

Problem 7

The following are the cross-sectional areas of an embankment at 30 m interval
$$
\begin{array}{llllllll}
\text { Distance in } m & 0 & 30 & 60 & 90 & 120 & 150 & 180 \\
\text { Area in } m^2 & 122 & 432 & 612 & 720 & 718 & 1020 & 1040
\end{array}
$$
Determine the volume of earth work by ( $i$ ) trapezoidal formula (ir) prismoidal formula

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
04:27

Problem 8

The areas within the contour lines at the site of a reservoir and along the proposed dam site are as follows:
$$
\begin{array}{llllllll}
\text { Contour in } m & 100 & 105 & 110 & 115 & 120 & 125 & 130 \\
\text { Area in } m^2 & 1250 & 1420 & 17300 & 20200 & 25200 & 32400 & 36780
\end{array}
$$

Assuming 100 m as bottom level of the reservoir and 130 m as full level, determine the capacity of the reservoir using trapezoidal and prismoidal rules.

Arwa  Ali
Arwa Ali
Numerade Educator