The parabolic segment

The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment

a) around its base
b) around its axis.

Correct result:

V₁ =  0 cm³
V₂ =  50.2655 cm³

Solution:

$$\begin{gathered} a=4\text{ cm } \\ v=6\text{ cm } \\ f(x)=q{x}^2 \\ f(a\mathrm{/}2)=q(a\mathrm{/}2{)}^2=v \\ 6=q\cdot 2^2 \\ {V}_1=q=6\mathrm{/}{2}^2={\displaystyle \frac{3}{2}}=1.5=0{\text{cm}}^3 \end{gathered}$$

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