Question

Extra Credit:
18
60°
V =
Hello guys I need help
Thank you

Answer 1

`\bold{V=7048.48 ft^3}`

Explanation:

Solution Given:

radius(r)=12

In right-angled triangle

Hypotenuse = 18

base angle =60°

Note:
In a right-angled triangle, we can use the trigonometric ratios sine, cosine, and tangent to relate the angles and sides of the triangle.
Here are the trigonometric ratios for a right-angled triangle:

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

`\boxed{\bold{sin(A) =( opposite)/(hypotenuse)}}`

Cosine (cos): The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

`\boxed{\bold{cos(A) = (adjacent)/(hypotenuse)}}`

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

`\boxed{\bold{tan(A) =( opposite)/(adjacent)}}`

Now for the question:

Over here the relation between opposite or height and hypotenuse is given by Sine, So using this formula:

`\bold{sin(60^0) =( opposite\:or\ height)/(18)}`

doing criss-cross multiplication:

Sin 60°*18=opposite or height

`(√(3))/(2)*18` =opposite or height

opposite or height(h)=
`9√(3)`

Again,

We have

`\boxed{\bold{Volume\:of\:cylinder= \pi * r^2 * h}}`

where:

π (pi) is a mathematical constant approximately equal to 3.14

r is the radius of the base of the cylinder

h is the height of the cylinder

Now Substituting value

`Volume = \pi * r^2 * h\\Volume=3.14*12^2*9√(3)\\Volume=\bold{7048.48 ft^3}`