# Tag Info

### How to intuitively see that the $\text{volume of a pyramid }= 1/3 \times (\text{ area of base}) \times (\text{height})$

Here is a visual explanation::
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### Finding the volume of a weird figure

The area of a circle of radius $1$ is $\pi,$ which we can approximate by adding the areas of rectangles between chords of the circle. For half a circle, we can just use the area of half of each ...
• 99.5k
Accepted

### Finding the volume of a weird figure

First of all, notice that the plane intersecting the cylinder at $\frac{\pi}{4}$ means that the. plane can be expressed as $$z=x$$ You want to find the volume of the solid region using a double ...
• 1,847

### Finding the volume of a weird figure

First of all, it is impossible that the formula for a volume is in $\frac23 r^2$ for a reason of homogeneity. It must be $\frac23 r^3$. Proof : Up to a rotation that does not change the volume one can ...
• 83.6k

### Areas versus volumes of revolution: why does the area require approximation by a cone?

That is because the volume approximation by the conical frusta is equivalent to that by the cylindrical disks in 3D, analogous to the area approximation by the trapeziums/trapezia is equivalent to ...
• 1,553
Accepted

### Calculate the volume section of sphere

From Mengchun Zhang comment's, I try answer my question as below. Given $r=2$ and $a=\sqrt{2}$, we have \begin{align*} &2hr=a^2+h^2\\ \iff & 4h=2+h^2\\ \iff & h^2-4h+2=0\\ \iff& h_{1,2}...
• 2,350