A small terrace at a hockey ground comprises of 10 steps each of which 20m long and built of solid concrete. Each step has a rise of 1 4 m and a tread of 1 2 m . What is the total volume of concrete required to build the terrace?

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A small terrace at a hockey ground comprises of 10 steps each of which 20m long and built of solid concrete. Each step has a rise of $14 m$ and a tread of $12 m$ . What is the total volume of concrete required to build the terrace?

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138 m 3

147.9 m 3

128.5 m 3

137.5 m 3

answer is D.

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Detailed Solution

Given that a small terrace of 10 steps each of which 20m long, the length of first step is 20 m, height is

14 m

and the base is

12 m

We have the following formulae,
Volume of cuboid

= l × b × h

Sum of n number of terms

S n = n 2 [2 a + (n − 1) d]

The volume of first step will be,

= 20 × 14 × 12 = 52 m 3

Then for second step,

l = 20 m; h = 14 + 14 = 12 m b = 12 m

Volume of the second step will be,

= 20 × 12 × 12 = 5 m 3

For third step,

l = 20 m b = 12 h = 34 m

Volume of the third step will be,

= 20 × 12 × 34 = 152 m 3

52 m 3, 5 m 3, 152 m 3 … … … . (10 terms)

are in A.P,
The first term and the common difference will be,

a = 52 d = 5 − 52 = 52

Since

n = 10

then the sum of volumes of 10 steps will be,

S 10 = 102 2 × 52 + (10 − 1) 52

= 5 5 + 9 × 52

= 5552

S 10 = 2752 = 137.5 m 3

Thus, the volume of 10 steps is

137.5 m 3

.
Therefore the correct option is 4.

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