Hello!
The cylinder shown has a lateral surface area of about 80 square inches. Which answer is closest to the height of the cylinder? Use 3.14 to approximate pi.
We have the following data:
Al (lateral surface area) = 80 in²
R (ratio) = 4 in
h (height) = ? (in inches)
Adopt : π ≈ 3.14
We apply the data to the formula, we have:
![A_l = 2*\pi*R*h](https://tex.z-dn.net/?f=A_l%20%3D%202%2A%5Cpi%2AR%2Ah)
![80 = 2*3.14*4*h](https://tex.z-dn.net/?f=80%20%3D%202%2A3.14%2A4%2Ah)
![80 = 25.12\:h](https://tex.z-dn.net/?f=80%20%3D%2025.12%5C%3Ah)
![25.12\:h = 80](https://tex.z-dn.net/?f=25.12%5C%3Ah%20%3D%2080)
![h = \dfrac{80}{25.12}](https://tex.z-dn.net/?f=h%20%3D%20%5Cdfrac%7B80%7D%7B25.12%7D)
![h = 3.18 \to \boxed{\boxed{h \approx 3.2\:in}}\:\:\:\:\:\:\bf\green{\checkmark}](https://tex.z-dn.net/?f=h%20%3D%203.18%20%5Cto%20%5Cboxed%7B%5Cboxed%7Bh%20%5Capprox%203.2%5C%3Ain%7D%7D%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5Cbf%5Cgreen%7B%5Ccheckmark%7D)
Answer:
≈ 3.2 inches
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![\bf\green{I\:Hope\:this\:helps,\:greetings ...\:Dexteright02!}\:\:\ddot{\smile}](https://tex.z-dn.net/?f=%5Cbf%5Cgreen%7BI%5C%3AHope%5C%3Athis%5C%3Ahelps%2C%5C%3Agreetings%20...%5C%3ADexteright02%21%7D%5C%3A%5C%3A%5Cddot%7B%5Csmile%7D)
Answer:
x = 45
Step-by-step explanation:
Given
= 9
Multiply both sides by 5
x = 5 × 9 = 45
Use the geometric mean for right triangles here. Like this
![\frac{9}{y}= \frac{y}{7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7By%7D%3D%20%5Cfrac%7By%7D%7B7%7D%20%20)
. Cross multiply to get
![y^{2}=63](https://tex.z-dn.net/?f=%20y%5E%7B2%7D%3D63%20)
, and
![y= \sqrt{63}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%7B63%7D%20)
. That simplifies down to
![y= \sqrt{9*7}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%7B9%2A7%7D%20)
. Pull out the 9 as a perfect square of 3 and you're left with
![y=3 \sqrt{7}](https://tex.z-dn.net/?f=y%3D3%20%5Csqrt%7B7%7D%20)
, first choice above.
(24*32)/(2*3)
(768)/(6)
=128
I hope this helped you!!