Sol.
We observe that the length and width of each
1
2
step are 50m and
m respectively.
1
4
m.
Height of 1st step =
Height of 2nd step =
1
4
+
1
4
m
=
2
4
m
Similarly,
3
4
m and so on.
Let, V1 , V2 , V3 , …, V15 respectively denote the volumes of the concrete required to build the first, second, third, …, fifteenth step.
Q. A small terrace at a football ground comprises of 15 steps each of which is 50 m long and
1
4
built of solid concrete. Each step has a rise of
m and a tread of
1
2
m. Calculate the
total volume of concrete required to build the terrace.
And,
∴
Height of 3rd step =
50m
1
4
m
1
2
m
1
4
m.
Height of 1st step =
Height of 2nd step =
1
4
+
1
4
m
=
2
4
m
3
4
m
Let, V1 , V2 , V3 , …, V15 respectively denote the volumes of the concrete required to build the first, second, third, …, fifteenth step.
V1
=
50
×
1
2
×
1
4
m3 ,
Height of 3rd step =
50m
1
4
m
1
2
m
We know, Volume = l × b × h
Q. A small terrace at a football ground comprises of 15 steps each of which is 50 m long and
1
4
built of solid concrete. Each step has a rise of
m and a tread of
1
2
m. Calculate the
total volume of concrete required to build the terrace.
Sol.
V2
=
50
×
1
2
×
2
4
m3 ,
V3
=
50
×
1
2
×
3
4
m3 ,
And so on
Q. A small terrace at a football ground comprises of 15 steps each of which is 50 m long and
1
4
built of solid concrete. Each step has a rise of
m and a tread of
1
2
m. Calculate the
total volume of concrete required to build the terrace.
Sol.
V1
=
50
×
1
2
×
1
4
m3 ,
V2
=
50
×
1
2
×
2
4
m3 ,
V3
=
50
×
1
2
×
3
4
m3
Total volume of the concrete
=
50
×
1
2
×
1
4
+
V1
+
V2
+
V3
+
…
+
V15
=
Similarly,
V15
=
50
×
1
2
×
15
4
m3 ,
50
×
1
2
×
2
4
+
50
×
1
2
×
3
4
+
50
×
1
2
×
15
4
…
+
=
50
×
1
2
1
4
+
2
4
+
3
4
+
…
+
15
4
m3
1
4
2
4
3
4
15
4
=
25
1
4
+
2
4
+
3
4
+
…
+
15
4
m3
=
25
4
[ 1
+
2
+
3
+
…
+
15 ]
m3
=
25
4
×
120
m3
=
750 m3
25
30
∴
The total volume of concrete required to build the terrace is 750 m3 .