What is the formula for the volume of a cone? (Use the word Pi instead of the symbol)

Mathematics

1 answer:

ira [324]3 years ago

8 0

Answer:

(1/3) Pi r^2 h

Step-by-step explanation:

The volume of a cone (or pyramid, for that matter) is 1/3 the area of the base times the height.

Cones have bases that are circles, so their areas are Pi r^2, usually written $\pi r^2$ , Pi times the radius squared.

$V=\frac{1}{3}\pi r^2h$

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Simplify 6x + 6 + 5x - 8. 11x - 2 11x + 2 9x

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Find the area of the shaded portion in the circle.

Anastasy [175]

See the attached picture to better understand the problem

we know that
the area of the shaded portion in the circle=area 1+area 2

step 1
find area 1
area 1=area of semi circle
area 1=pi*r²/2
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radius r=12/2----> 6 units

r=6 units
area 1=pi*6²/2----> 56.52 units²

step 2
find the area 2

area 2=area sector CADC-area triangle ACD

in the right triangle ABC
BC=3
AC=r-----> AC=6
AB=?
applying Pythagoras Theorem
AC²=AB²+BC²------> AB²=6²-3²-----> AB²=27----> AB=3√3 units
area triangle ACD=b*h/2
b=2*3√3---> 6√3 units
h=3 units
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find the angle ACB
tan ∠ACB=AB/BC-----> 3√3/3---> √3
∠ACB=arc tan (√3)-----> 60°

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area 2=area sector CADC-area triangle ACD
area 2=37.68-15.59----> 22.09 units²

step 3
the area of the shaded portion in the circle=area 1+area 2
the area of the shaded portion in the circle= 56.52 +22.09----> 78.61 units²

the answer is
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