A small terrace at a football ground comprises of 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.

Solution: Volumeof 1st step=41⋅21⋅50=850Volume of 2nd step=42⋅21⋅50=8100Volume of 3rd step=43⋅21⋅50=8150Volume are in APSn=2n(2a+(n−1)d)S15=215(2(850)+(15−1)50)S15=750m3

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A small terrace at a football ground comprises of 15 steps eac

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A small terrace at a football ground comprises of 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 of 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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Text solutionVerified

Solution: Volumeof 1st step=

\frac{1}{4} \cdot \frac{1}{2} \cdot 50 = \frac{50}{8}

Volume of 2nd step=

\frac{2}{4} \cdot \frac{1}{2} \cdot 50 = \frac{100}{8}

Volume of 3rd step=

\frac{3}{4} \cdot \frac{1}{2} \cdot 50 = \frac{150}{8}

Volume are in AP

S_{n} = \frac{n}{2} (2 a + (n - 1) d)

S_{15} = \frac{15}{2} (2 (\frac{50}{8}) + (15 - 1) 50)

S_{15} = 750 m^{3}

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Question Text	A small terrace at a football ground comprises of 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
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A small terrace at a football ground comprises of 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

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A small terrace at a football ground comprises of 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.