The volume of each block is $V=\frac{1}{2}\times\frac{1}{4}\times 50=\frac{25}{4} \text{m}^3 .$ Now, how many blocks are there? Notice that at the first step, there is one block, at the second step, there are two blocks, at the third step three blocks, and so on, until the fifteenth step, which has 15 blocks. This forms an arithmetic progression, with $a_1=1, a_{15}=15, n=15$ and $d=1$ . Therefore, the total number of blocks is $S=\frac{n}{2}(a_1+a_n)=\frac{15}{2}(1+15)=120.$ Therefore, the total volume of the blocks is $V_{\text{total}}=\text{number of blocks} \times \text{volume of each block}=120 \times \frac{25}{4} \text{m}^3=\boxed{750\text{ m}^3}.$

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At first step we need to construct 1 block, at second step 2 blocks and third step 3 blocks and so on up to 15th step.

Total no of Blocks = 1+2+3+.......+15 = 15*(15+1)/2 = 120

Volume of one block = 50 1/2 1/4 = 6.25 m^3

Total volume = 120 x 6.25 = 750 m^3

First, you have to solve for how many rectangular sections there are. There will be 1 for the first step, 2 for the second, all the way until the 15th step. Thus there are a total of 120 blocks of $50 \times 0.5 \times 0.25$ dimensions. Therefore the area is $\boxed{750}$ .

The volume of the Concrete steps can be viewed as a prism.

Therefore its volume can be calculated by the following formula:

Volume = Cross-sectional Area * Depth

The Cross-sectional area can be calculated with the help of triangular numbers, As the number is 15 the following equation is pretty straight forward:

$\frac { n(n+1) }{ 2 } \quad \rightarrow \quad \frac { 15\times 16 }{ 2 } \quad =\quad 120$ .

This formula calculates for a unit, whose value is one, so evidently it needs to be scaled down. In this case the unit is an $\frac { 1 }{ 8 }$ of the square metre.

$Cross\quad sectional\quad area\quad =120\times \frac { 1 }{ 8 } =15m^{2}$

Finally plugging the 50 metres into the formula gives the answer: $Volume\quad =\quad 50\times 15\quad =\quad \boxed{750m^{3}}$

{(15 16)/2} {50 (1/2) (1/4)}=750

50x(15/8+14/8+13/8.....+1/8) = 50x((15x16)/2)/8 = 50x15 = 750

V = .5 x .25 x 50 = 6.25 and in each concrete block, we know that its height increased by 1 consecutively, so the sum of first 15 concrete blocks was 120. Therefore, 6.25 x 120 = 750 :)

V = 1 x (w x l x h) + 2 x(w x l x h) ......+ 15 x (w x l x h) = 1 x (1/4 x 1/2 x 50 ...+ 15 x (1/4 x 1/2 x 50) V = 750 cu.meter

easy...........

volume of a block = v = 50 0.5 0.25 = 6.25m3 the total volume of 15 steps is = 15v + 14v + 13v + 12v+....+v = v (1+2+3+4+....15) = (15)(16/2)*v = 750m3

The steps are all equal, as they are with the spaces beneath them so we can use the triangle numbers .

The fifteenth triangle number is 120. Found using (1/2 ( n x (n+1))

Each step has a cross section of 1/8 m^2.

Cross Sectional Area of the steps = 120x1/8 = 15 m^2

Volume = Cross Sectional Area x Length = 15 x 50 = 750 m^3

You can count the area from the top where the are is $50 \times 0.25 \times 0.5 = 6.25$

The length $50m$ and rise $.25m$ never changes, the tread only changes increased every step in the direction of gravitational force. that is

$50 \times 0.25 \times 1 = 12.5$

$50 \times 0.25 \times 1.5 = 18.75$

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and so on.......

After summing up all the result we get $750m^2$

volume of 1 block = 50 1/4 1/2 = 25/4

total no. of blocks = 120

total volume = 25/4 * 120 = 750

The length,width is same for all.but height goes .25m up every time. V=50 x .5 x (0.25+0.5+0.75+.......+3.75)

Imagine that the terrace is actually a rectangular prism 50 m x 7.5 m (15/2) x 3.75 m (15/4). The volume of the entire prism would be 1406.25 cubic meters. The volume of concrete on the terrace is 1/2 of 1406.25 cu. m. + the sum of the area of 15 right triangles with base .25 m and height .5 m. 1/2 of 1406.25 is 703.125. Each step (right triangle) has a volume of (.25 m x .5 m x 50 m) / 2 , or 3.125 cu. m. 3.125 cu m x 15 steps = 46.875 cu m. 703.125 cu m + 46.875 cu m = 750 cubic meters

number of staircase would be 1+2+3+... +15 as a staircase cannot be in air. So for 2nd staircase onwards we need stairs below it as well. so adding these using formula for sum of first n natural numbers we get, S=n(n+1)/2 =15(16)/2 =120 therefore total volume V=120 50 (1/4)*(1/2) =750

we have volume of one step=1/4x1/2x50=6.25

since there are 15 steps so the height of each steps is 1/4 more than the last

so we can say , volume of second step is twice the first step and third step is thrice the first and so on......

by this we can write, the total volume of steps as 6.25+2x6.25........+15x6.25

which can be written as 6.25(1+2+3......+15)

which is 6.25x120

which comes to 750

Total no of 50x1/4*1/2 blocks required=1+2+3+...+15=120 So, volume=120x(1/2)x(1/4)x(50)=750

dividing it horizontally, volume of lowset step = (0.5 15) 0.25 50 for last but one step (ie 14th step): (0.5 14) 0.25 50 and so on.. for last step: (0.5 1) 0.25*50

hence total volume = (0.5 0.25 50*(1+2+3---+14+15)) = 750 m3

simple, volume = 50 * 1/2 * ( 1/4 +2/4 + 3/4 + ..........+15/4 ) = 50 * 15 * 16 / ( 2 * 4 * 2 ) =750.

Look at the cross-section of the steps. Clearly, Volume = Area of cross section x 50.

Divide the cross section into 15 parts, each part being a rectangle formed by the extension of the rise of each step. Then,

Area of cross section = (.25x.5) + (.25x2x.5) + (.25x3x.5)....+(.25x15x.5) The sum can easily be calculated by the concept of arithmetic progression. It turns out to be 15.

Thus the volume is 15x50 = 750 cubic meters.