Find the surface area of the prism.

Mathematics

1 answer:

Anton [14]3 years ago

6 0

Answer:

$\text{D. }464\:\mathrm{ft^2}$

Step-by-step explanation:

The surface area of the prism consists of four rectangles and two trapezoids. The sum of the areas of these polygons will give the total surface area of the prism:

Rectangle 1 (top base): $12\cdot 14=168$

Rectangle 2 (bottom base): $6\cdot 14 = 84$

Trapezoids 1 and 2 (lateral): $2\cdot 9 \cdot 4=72$

Rectangles 3 and 4 (lateral): $2\cdot 14\cdot 5=140$

Thus the total surface area is equal to

$168+84+72+140=\boxed{\text{D. }464\:\mathrm{ft^2}}$

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Let the region R be the area enclosed by the function f(x)=ln(x) and g(x)= 1/2x-2. Find the volume of the solid generated when t

Neporo4naja [7]

Answer:

$V=61.66$

Step-by-step explanation:

This problem can be solved by using the expression for the Volume of a solid with the washer method

$V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx$

where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).

Before we have to compute the limits of the integral. We can do that by taking f=g, that is

$f(x)=g(x)\\ln(x)=\frac{1}{2}x-2$

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)

x1=0.14

x2=8.21

and because the revolution is around y=-5 we have

$R=ln(x)-(-5)\\r=\frac{1}{2}x-2-(-5)\\$