The required equation of the surface area of the cylinder is 
<u>Solution:</u>
Let "r" be the radius of cylinder and "h" be the height.
Formula for surface area is:
where 
is surface of two bases of cylinder and 
is surface of mantle.
From the given, the height of the gift box is three times the radius, i.e 
On substituting the given values in the formula we get,
![S = 2\times\pi[(3x+4)^2 + (9x+12)\times(3x+4)]](https://tex.z-dn.net/?f=S%20%3D%202%5Ctimes%5Cpi%5B%283x%2B4%29%5E2%20%2B%20%289x%2B12%29%5Ctimes%283x%2B4%29%5D)
![\Rightarrow S=2\pi[(3x^2)+2\times3x\times4+4^2]+[(9x\times3x)+12\times3x+36x+48]](https://tex.z-dn.net/?f=%5CRightarrow%20S%3D2%5Cpi%5B%283x%5E2%29%2B2%5Ctimes3x%5Ctimes4%2B4%5E2%5D%2B%5B%289x%5Ctimes3x%29%2B12%5Ctimes3x%2B36x%2B48%5D)
![\Rightarrow S=2\pi[9x^2+24x+16]+[21x^2+36x+36x+48]](https://tex.z-dn.net/?f=%5CRightarrow%20S%3D2%5Cpi%5B9x%5E2%2B24x%2B16%5D%2B%5B21x%5E2%2B36x%2B36x%2B48%5D)
![\Rightarrow S=2\pi[9x^2+24x+16+21x^2+72x+48]\rightarrow2\pi[30x^2+96x+64]](https://tex.z-dn.net/?f=%5CRightarrow%20S%3D2%5Cpi%5B9x%5E2%2B24x%2B16%2B21x%5E2%2B72x%2B48%5D%5Crightarrow2%5Cpi%5B30x%5E2%2B96x%2B64%5D)
On multiplying 
inside the brackets we get,
![\Rightarrow S=[60\pi x^2+192\pi x+128\pi]](https://tex.z-dn.net/?f=%5CRightarrow%20S%3D%5B60%5Cpi%20x%5E2%2B192%5Cpi%20x%2B128%5Cpi%5D)
Hence, the required equation is
The answer to that problem is A
Answer:
Step-by-step explanation:
Let b represent the number of cups of butter needed.
Let s represent the number of cups of sugar needed.
Let o represent the number of cups of oat needed.
Let f represent the number of cups of flour needed.
The recipe calls for two times as many cups of sugar as butter. It means that
s = 2b
Two times as many cups of oats as sugar. It means that
o = 2s
Two times as many cups of flour as oats. It means that
f = 2o
If Duane puts in one cup of butter, it means that b = 1
Therefore,
s = 2 × 1 = 2 cups
o = 2s = 2 × 2 = 4 cups
f = 2o = 2 × 4 = 8 cups
Therefore, he needs to add 8 cups of flour
Answer:
Step-by-step explanation:
The equation of a circle is:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
Given that (h, k) is (-3, -5) and r = 6:
(x + 3)² + (y + 5)² = 6²
(x + 3)² + (y + 5)² = 36
