The formula for a cone is given as:
<span>V = π r^2 h / 3 --->
1</span>
Where,
V = volume of the cone
r = radius of the circle base of the cone
h = is the perpendicular length from the center of the
base of the cone to the tip at the top
It was given that:
h = d
but d = 2 r, therefore:
h = 2 r
Substituting this to equation 1:
<span>V = π r^2 (2 r) / 3 </span>
V = 2 π r^3 / 3
Since r = x, the answer from the choices is:
<span>2πx3</span>
Measure of one of the vertical angle is 156°
Solution:
The measure of angles given are (x + 104)° and 3x°.
The given angles are vertical in order.
If two lines meet at a point, then the angle formed in vertical positions are equal.
That is vertically opposite angles are equal.
⇒ 3x° = (x + 104)°
⇒ 3x° = x° + 104°
Subtract x° on both sides of the equation to equal the expression,
⇒ 3x° – x° = x° + 104° – x°
⇒ 2x° – x° = 104°
⇒ 2x° = 104°
Divide both sides of the expression by 2, we get
⇒ x° = 52°
Substitute x° = 52° in one of the vertical angle.
3x° = 3 × 52° = 156° (or)
x° + 104° = 52°+ 104° = 156°
Hence the measure of one of the vertical angle is 156°.
Answer:
<u>Simplify</u><u> </u><u>:</u><u>-</u>
6. 2
7. (3x^2 -9x - 2)/(x^2 -3x -10)
8. (x +4)^2/(x -4)(x-2)
9. 4x/5(x -5)
10. 2(3x -5)/x^2 -4
11. 2
<u>triangle :-</u>
1.
sin A = 4/5
cos A = 3/5
tan A = 4/3
sin B = 3/5
cos B = 4/5
tan B = 3/4
2.
sin A = 1/3
cos A = (root 2)/3
tan A = 1/(root 2 )
sin B = (root 2)/ 3
cos B = 1/3
tan B = (root 2 )/1
3.
sin A = 1/(root 2)
cos A = 1/(root 2)
tan A = 1
sin B = 1/(root 2)
cos B = 1/(root 2)
tan B = 1
4.
sin A = 5/13
cos A = 12/13
tan A = 5/12
sin B = 12/13
cos B = 5/13
tan B = 12/5