Answer:
Option A. ![40\ cm](https://tex.z-dn.net/?f=40%5C%20cm)
Step-by-step explanation:
we know that
The lateral area of a cone is equal to
![LA=\pi rl](https://tex.z-dn.net/?f=LA%3D%5Cpi%20rl)
we have
![LA=400\pi \ cm^{2}](https://tex.z-dn.net/?f=LA%3D400%5Cpi%20%5C%20cm%5E%7B2%7D)
![r=10\ cm](https://tex.z-dn.net/?f=r%3D10%5C%20cm)
substitute and solve for l (slant height)
![400\pi=\pi (10)l](https://tex.z-dn.net/?f=400%5Cpi%3D%5Cpi%20%2810%29l)
simplify
![400=(10)l](https://tex.z-dn.net/?f=400%3D%2810%29l)
![l=400/10=40\ cm](https://tex.z-dn.net/?f=l%3D400%2F10%3D40%5C%20cm)
Answer:
The height of the cylinder is 4x units.
Step-by-step explanation:
volume of a cylinder = nr^2h
n = 22/7
r = radius = x/2
Let illustrate with an example. If the diameter of a cylinder is 6 and the volume is 6^3 = 216. The radius = 6/2 = 3
n3^2 x h = 216
h = 216/9 = 24
so the height is 4 times the diameter
Area of the base = nr^2
1/2^2 x x = 1/4 pi x^2
Answer:
a ) 2¹/2
Step-by-step explanation:
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Answer:
7x13=91
Step-by-step explanation:
Answer:
The variance of these investment returns is 74
Step-by-step explanation:
Given:
Series = 10, 30, 15, 5, 20
To Find:
variance of a series = ?
Solution:
The variance of the series = ![Var\left(X\right)=\sum _{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n}](https://tex.z-dn.net/?f=Var%5Cleft%28X%5Cright%29%3D%5Csum%20_%7Bi%3D1%7D%5En%5Cfrac%7B%5Cleft%28x_i-%5Cbar%7Bx%7D%5Cright%29%5E2%7D%7Bn%7D)
![\bar{x} = \frac{10+30 +5+15 + 20}{5}](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20%3D%20%5Cfrac%7B10%2B30%20%2B5%2B15%20%2B%2020%7D%7B5%7D)
![\bar{x} = \frac{80}{5}](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20%3D%20%5Cfrac%7B80%7D%7B5%7D)
![\bar{x} =16](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20%3D16)
Now
![(10 -16)^2 + (30 -16)^2 + (5 -16)^2 +(15 -16)^2 +(20 -16)^2](https://tex.z-dn.net/?f=%2810%20-16%29%5E2%20%2B%20%2830%20-16%29%5E2%20%2B%20%285%20-16%29%5E2%20%2B%2815%20-16%29%5E2%20%2B%2820%20-16%29%5E2)
= ![(-6)^2 + (14)^2 + (-11)^2 + (-1)^2+ (-4)^2](https://tex.z-dn.net/?f=%28-6%29%5E2%20%2B%20%2814%29%5E2%20%2B%20%28-11%29%5E2%20%2B%20%28-1%29%5E2%2B%20%28-4%29%5E2)
= 36 + 196 +121 + 1+ 16
= 370
Now
= 74