B = 2h
Area = 121
1/2 × b × h = 121
1/2 × 2h × h = 121
h × h = 121
h^2 = 121
h = square root of 121
h = 11
The height is 11 kilometers
Answer:
LCM means Lowest Common Multiple
GCF means Greatest Common Factor
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Answer:
Doubling the radius and the height of a right cylinder will increase the value of its surface area by a factor of 4
Step-by-step explanation:
Mathematically, the surface area of a right cylinder can be calculated using the formula;
A = 2 π r (r + h)
now let’s double the radius and the height.
Our new r becomes 2r and our new height becomes 2h. Substituting these into the area formula, we have
A = 2 π (2r)( 2r+ 2h)
Let’s factor out all the 2 , we have
A = 4 π r (2(r+h))
A = 8 π r( r + h)
we can see that the value of the area has been increased by a factor of 4
The differential of volume can be a disk of radius (7-√(7x)) and thickness dx, so is
... dV = π·r²·dx = π(7-√(7x))²·dx
Integrated over the region 0 ≤ x ≤ 7, this becomes
![V=\displaystyle \int_{0}^{7}{\pi\left(7-\sqrt{7x}\right)^{2}\,dx}\\\\=\pi\left[49x-\dfrac{28x\sqrt{7x}}{3}+\dfrac{7x^2}{2}\right]\limits_{0}^{7}\\\\=49\pi\left(7-\dfrac{28}{3}+\dfrac{7}{2}\right)\\\\V=343\cdot \dfrac{\pi}{6}\approx 179.59438](https://tex.z-dn.net/?f=%20V%3D%5Cdisplaystyle%20%5Cint_%7B0%7D%5E%7B7%7D%7B%5Cpi%5Cleft%287-%5Csqrt%7B7x%7D%5Cright%29%5E%7B2%7D%5C%2Cdx%7D%5C%5C%5C%5C%3D%5Cpi%5Cleft%5B49x-%5Cdfrac%7B28x%5Csqrt%7B7x%7D%7D%7B3%7D%2B%5Cdfrac%7B7x%5E2%7D%7B2%7D%5Cright%5D%5Climits_%7B0%7D%5E%7B7%7D%5C%5C%5C%5C%3D49%5Cpi%5Cleft%287-%5Cdfrac%7B28%7D%7B3%7D%2B%5Cdfrac%7B7%7D%7B2%7D%5Cright%29%5C%5C%5C%5CV%3D343%5Ccdot%20%5Cdfrac%7B%5Cpi%7D%7B6%7D%5Capprox%20179.59438%20%20)
