9514 1404 393
Answer:
(b) 458 ft²
Step-by-step explanation:
The total area is the sum of the L-shaped front and back areas and the areas of the 6 rectangular faces.
The front L-shaped area can be considered to be a 12 ft × 12 ft square with a 5 ft × 7 ft rectangle cut from the upper left corner. Its area is then ...
(12 ft)(12 ft) -(5 ft)(7 ft) = (144 -35) ft² = 109 ft² . . . . front area
__
The sum of the areas of the rectangular faces is the product of the width of the figure (5 ft) and the perimeter of the L-shaped face. That perimeter is the sum of the edge lengths. Starting from the lower-left corner and working clockwise, we find the perimeter to be ...
7 ft + 7 ft + 5 ft + 5 ft + 12 ft + 12 ft = 48 ft
Then the sum of rectangular face areas is ...
(48 ft)(5 ft) = 240 ft² . . . . rectangular face area
The total surface area is then ...
2×front area + rectangular face area
= 2×109 ft² +240 ft² = 458 ft² . . . . total surface area
Answer:
it is the square root of 145
Step-by-step explanation:
use distance formula
Explanation:
Let 
and 
. The differential volume dV of the cylindrical shells is given by
![dV = 2\pi x[f(x) - g(x)]dx](https://tex.z-dn.net/?f=dV%20%3D%202%5Cpi%20x%5Bf%28x%29%20-%20g%28x%29%5Ddx)
Integrating this expression, we get
![\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%20%3D%202%5Cpi%5Cint%7Bx%5Bf%28x%29%20-%20g%28x%29%5D%7Ddx)
To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:
We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:
or
Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is
The improper fraction -8/3 is equivalent
