Question

What is the volume of a 6m deep tank having rectangular shaped top 6 m 4 m and bottom 4 m 2 m computed through the use of prismoidal formula?

Answer 1

Answer:

ans is 92m3

Step-by-step explanation:

Answer 2

The volume of the tank with the rectangular-shaped top and bottom by using the prismoidal formula is 92 m³.

Step-by-step explanation:

It is given that,

There is a tank which has a top and bottom in the shape of a rectangle

The dimension of the rectangular top = 6 m * 4m

The dimension of the rectangular bottom = 4 m * 2 m

Depth of the tank = 6 m

The Prismoidal Formula applies to volumes of all geometric solids that can be considered as prismoids. This formula is also known as the Simpson’s Rule for Volumes.  

The prismoidal formula for the volume of a solid is given by,

V = (L/6) * [A1 + 4Am + A2]

Where

L = depth of the tank

A1 = area of the top section

A2 = area of the bottom section

Am = area of the middle section which is based on the linear measurements at the middle

Now, according to the question here we have

A1 = area of rectangular top = 6 * 4 = 24 m² …… (i)

A2 = area of rectangular bottom = 4 * 2 = 8 m² …… (ii)

Am = area of the middle section of the tank = $\frac{6+4}{2} * \frac{4+2}{2}$ = 5 * 3 = 15 m² …… (iii)

Therefore, substituting values from (i), (ii) & (iii) in the prismoidal formula, we get

V = (6/6) * [24 + 4*15 + 8] = 24 + 60 + 8 = 92 m³

Thus, the volume of the tank is 92 m³.

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Also View:

Using prismoidal method, what is the volume (cubic metre) of earthwork required for 10 m deep pit, if the top and bottom dimensions are 4 m x 8 m and 8 m x 16 m respectively?

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