areageometry
A circular pie was cut into 9 pieces in a unique way. First, a circle with a radius of 5 cm was cut from the center of the pie. Then the remaining pie was cut into eight congruent pieces. If the area of the top of each of the 9 pieces is equal, what is the diameter of the pie?
It's been years since I've done math and my work posted this question today for pie day and it's bothering me that I can't remember how to solve it.
The following is the process to find the surface area of rectangular box with its top side missing.
Let's call the side of the square base $s$ and let's call the height of the prism $h$.
Normally you have 6 sides. However, now you only have 5.
You have 4 sides of area $hs$ and one base of area $s^{2}$.
Therefore, $SA = hs + s^{2}$.
Feel free to plug in the given values.
The following is the process to find the surface area of cylinder with its top side missing.
Let's call the diameter of the circle base $D$ and let's call the height of the prism $h$.
The lateral surface area is $\frac{D}{2} h \pi$. The area of the base is the area of a circle: $\pi r^{2}$. Adding these two expressions, the surface area is $\frac{D}{2} h \pi + \pi r^{2}$.
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Best Answer
The area of a circle is $\pi\cdot r^2$ so area of small circle is $25\pi$
So, the area of all the congruent pieces is $25\pi$
$9\cdot25\pi = 225 \pi$
Divide by $\pi$, then take the root to get
$r=15$
So, diameter is $30$.