Answer:
h = 9 units of length
Step-by-step explanation:
Volume of a circular right cone is:
V(c) = (1/3)*Area of the circular base * h
Where h is the height of the cone, then
V(c) = (1/3) * π * r² * h
And we have that V(c) = 108*π
Then:
108 * π = (1/3) * π * r² * h (1)
We know diameter of the circular base is 12 units, according to that
r = d/2 ⇒ r = 12/2 r = 6 units
Then:
108 * π [ cubic units ] = (1/3) * π * (6)² * h [square units] [ units of length]
When simplifying we have to take into account that in order to keep last equation h needs to have units of length
Therefore:
108 = (1/3) * 36 * h
h = ( 108* 3 )/ 36
h = 9 units of length
Answer:
The measure of ∠G is 59°
Step-by-step explanation:
<em>When </em><em>two secants</em><em>, intersect at </em><em>a point outside a circle</em><em> then the </em><em>measure of the angle formed between them</em><em> is </em><em>one-half the positive difference of the measures of the intercepted arcs.</em>
<em></em>
In the given figure
∵ GT is a secant that intersects the circle at points H and T
∵ GE is a secant that intersects the circle at points F and E
∴ The intercepted arcs are HF and TE
∵ GT ∩ GE at G
∵ Point G is outside the circle
→ By using the rule above
∴ m∠G = 
(m arc TE - m arc HF)
∵ m arc TE = 175°
∵ m arc HF = 57°
→ Substitute them in the rule above
∵ m∠G = (175 - 57) = (118)
∴ m∠G = 59
∴ The measure of ∠G is 59°
You have to use distributive property. Multiply the numbers outside of the parenthesis by the numbers inside. For example, you would multiply 0.4 by 2x first, then multiply it by 1/2. You should get two answers. Write them down in this form: first answer + second answer. Then do the same for the other side of the equal sign, but leave the - 4 alone. If you need more help, let me know
B
Because first “reduce” both sides of the top equation by the same to simplify it. See what both sides have in common.
They both have 3 long rectangles and 2 Sm. Squares.
That leaves, 2 long rectangles = 6 squares.
Which means that each long rectangle = 3 squares
