Cone details:
Sphere details:
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From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.
<u>Using Pythagoras Theorem</u>
(a)
TO² + TU² = OU²
(h-10)² + r² = 10² [insert values]
r² = 10² - (h-10)² [change sides]
r² = 100 - (h² -20h + 100) [expand]
r² = 100 - h² + 20h -100 [simplify]
r² = 20h - h² [shown]
r = √20h - h² ["r" in terms of "h"]
(b)
volume of cone = 1/3 * π * r² * h
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To find maximum/minimum, we have to find first derivative.
(c)
<u>First derivative</u>

<u>apply chain rule</u>

<u>Equate the first derivative to zero, that is V'(x) = 0</u>




<u />
<u>maximum volume:</u> <u>when h = 40/3</u>


<u>minimum volume:</u> <u>when h = 0</u>


Answer:
360 in ^3
Step-by-step explanation:
The volume is given by
V = l*w*h
= 8 * 5 * 9
= 360 in ^3
Triangles are congruent if they have the same (Shape and Size).
Answer:
x = 750
Explanation:
25x = 30
1. Multiply 25 by 30
25 * 30 = 750
2. Divide 750 by 25
750/25 = 30
3. Divide 750 by 30
750/30 = 25
Therefore, x = 750
Answer:
0
Step-by-step explanation:
Its basically infinite because 9 divided by 3 is how many times 3 goes into 9 so 0 divided by 0 is how many times 0 goes into 0 which is infinite.