A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to
Since the area of the circle is the area of the
square, the volume of the cone equals
the area of the square is
or 7
402
o the volume of the pyramid or - Alenchor
arh.
Cross section
r
o the volume of the pyramid or
+(1200)
2n.
o the volume of the pyramid or z { nºm) or
7
2r
2r
22h.
0 Į the volume of the pyramid or = { 29°m) oraz
arh.
m no

Answer on Question #47534 – Math – Geometry

How to prove the volume formula of con is 1/3×π×r^2×h;without using

integration?

Solution.

Suppose we take a slice of the pyramid with the cone inside, from some way up

the pyramid. This will look like a square with a circle fitting inside. Radius of the

cone at this point, will be x.

The area of the circle is

The area of the square is × =

The ratio of the circle to the square is

.

The same is true for every slice we take: the area of the circle is

of the area

of the square.

So, the volume of the cone will be

the volume of the pyramid.

The pyramid's volume is

.

So the cone's volume is

∗

=

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet