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3 years ago

A cone fits inside a square pyramid as shown. For

Mathematics

1 answer:

likoan [24]3 years ago

6 0

Answer:

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

∗

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3 years ago

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3 years ago

If tan0=-3/4 and 0 is in quadrant IV, cos20= (33/25, -17/25, 32/25, 7/25, 24/25?) and tan20= (24/7, -24/7, 7/25, -7/25, 13/7, -1

Oksana_A [137]

Answer:

cos(2θ) = 7/25
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Sometimes, it is easiest to let a calculator do the work. (See below)

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You can also use the identities ...

cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)

cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

cos(2θ) = 7/25

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tan(2θ) = -24/7

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