A small terrace at a football ground comprises 15 steps each of which is 50 m long and built of solid concrete.Each step has a rise of 41m and a tread of 21m. Calculate the total volume of concrete required to build the terrace.

Dimensions in 1st step = 50×0.25×05 mVolume of first step =6.25 cubic mDimensions of second step= 50×0.5×05mVolume of 2nd step =12.5 cubic mDimensions of 3rd step = 50×0.75×05 mVolume of 3rd step =18.75 cubic mNow, we have a=6.25,d=6.25 and n=15Sum of 15 terms can be calculated as follows:S15=215[2×6.25+14×6.25] =215×100=750Volume of concrete =750 cubic m

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A small terrace at a football ground comprises 15 steps each o

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A small terrace at a football ground comprises $15$ steps each of which is $50$ m long and built of solid concrete.
Each step has a rise of $\frac{1}{4}$ m and a tread of $\frac{1}{2}$ m. Calculate the total volume of concrete required to build the terrace.

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A small terrace at a football ground comprises

15

steps each of which is

50

m long and built of solid concrete.
Each step has a rise of

\frac{1}{4}

m and a tread of

\frac{1}{2}

m. Calculate the total volume of concrete required to build the terrace.

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Discuss this question LIVE

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Text solutionVerified

Dimensions in

1^{s t}

step

=

50 \times 0.25 \times 05

Volume of first step

= 6.25

cubic m

Dimensions of second step

=

50 \times 0.5 \times 05

Volume of

2^{n d}

step

= 12.5

cubic m

Dimensions of

3^{r d}

step

=

50 \times 0.75 \times 05

Volume of

3^{r d}

step

= 18.75

cubic m

Now, we have

a = 6.25, d = 6.25

and

n = 15

Sum of

15

terms can be calculated as follows:

S_{15} = \frac{15}{2} [2 \times 6.25 + 14 \times 6.25]

= \frac{15}{2} \times 100 = 750

Volume of concrete

= 750

cubic m

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Question Text	A small terrace at a football ground comprises $15$ steps each of which is $50$ m long and built of solid concrete. Each step has a rise of $\frac{1}{4}$ m and a tread of $\frac{1}{2}$ m. Calculate the total volume of concrete required to build the terrace.
Answer Type	Text solution:1
Upvotes	150

A small terrace at a football ground comprises 15 steps each of which is 50 m long and built of solid concrete.Each step has a rise of 41​m and a tread of 21​m. Calculate the total volume of concrete required to build the terrace.

Text solutionVerified

Practice questions from similar books

A small terrace at a football ground comprises $15$ steps each of which is $50$ m long and built of solid concrete.
Each step has a rise of $\frac{1}{4}$ m and a tread of $\frac{1}{2}$ m. Calculate the total volume of concrete required to build the terrace.