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MathsKid007

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We can find the exact volume of any shape using:

V= \(\displaystyle int[a,b] A(x) dx\)

Where,A(x)is the cross-sectional area at height x

and [a,b] is the height interval

We know that the horizontal cross-sections are hexagonal

\(\displaystyle ∴A=(3√3)/2 a^2\)

Where a,is the length of a side

Write the side length a,at height x

a= s

\(\displaystyle ∴A=(3√3)/2 s^2\)

\(\displaystyle V= int[0,h](3√3)/2 x^2 dx\)

\(\displaystyle V= (3√3)/2 int[0,h]x^2 dx\)

\(\displaystyle = (3√3)/2*x^3/3\)

\(\displaystyle =[(√3 x^3)/2] [0,h]\)

\(\displaystyle V=(√3 h^3)/2\)

**This is what i have so far**We can find the exact volume of any shape using:

V= \(\displaystyle int[a,b] A(x) dx\)

Where,A(x)is the cross-sectional area at height x

and [a,b] is the height interval

We know that the horizontal cross-sections are hexagonal

\(\displaystyle ∴A=(3√3)/2 a^2\)

Where a,is the length of a side

Write the side length a,at height x

a= s

\(\displaystyle ∴A=(3√3)/2 s^2\)

\(\displaystyle V= int[0,h](3√3)/2 x^2 dx\)

\(\displaystyle V= (3√3)/2 int[0,h]x^2 dx\)

\(\displaystyle = (3√3)/2*x^3/3\)

\(\displaystyle =[(√3 x^3)/2] [0,h]\)

\(\displaystyle V=(√3 h^3)/2\)

**Is this correct?**