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dustinralph9768
20.03.2020 •
Mathematics
This robotic arm is made up of two cylinders with equal volume and two triangular prism hands. The volume of each hand is
1
2 r ×
1
3
r ×
2r, where r is the radius of the cylinder's base. What fraction of the total volume do the robotic hands take up?
Solved
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Ответ:
Step-by-step explanation:
Since the height isn't given, we assume it to be "h" (of cylinders). And the answer will be in terms of "r" and "h".
The area of 1 arm is given, so the area of 2 arms would be:
Now, area of 2 cylinders would be the formula:
So, total area is A_arm PLUS A_cyl. The fractional area the arms are would be gotten by taking expression A_arm divided by A_total.
Shown below:
We simplify further:
THis is the answer.
Ответ:
r/(9.42H + r),
where H is each cylinder's height
Step-by-step explanation:
Volume of hands:
2 × ½t × ⅓r × 2r = ⅔r³
Let H be the height of each cylinder
Total volume:
2(3.14×r²×H) + ⅔r³
(6.28H + ⅔r)r²
Ratio:
[⅔r³] ÷ (6.28H + ⅔r)r²
r ÷ (9.42H + r)
r/(9.42H + r)
Ответ:
It is the tenths place. 109.7 is greater than 109.6