I need help on this asap please
2 answers:
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Answer:
V_t = 72 ft^3
Step-by-step explanation:
Solution:-
- The complete question is given in the attachment.
a)
- The length of the smaller rectangular prism ( l ) is the side that runs along horizontal to the page and marked by l = 4 feet.
- The width of the smaller rectangular prism ( w ) is the side that protrudes out of the page, and also share the same dimension as the larger rectangular prism and marked by w = 2 feet.
- The height of the smaller rectangular prism ( h ) is the side that runs vertical to the page and marked by h = 3 feet.
- So the dimensions of the smaller rectangular prism are:
( l , w , h ) = ( 4 , 2 , 3 ) feet
- Similarly, for the larger rectangular prism:
- The length of the larger rectangular prism ( L ) is the side that runs along horizontal to the page and the sum of smaller and upper exposed face length, totaling to L = ( 4 + 4 ) = 8 feet.
- The width of the larger rectangular prism ( W ) is the side that protrudes out of the page, and also share the same dimension as the larger rectangular prism and marked by W = 2 feet.
- The height of the larger rectangular prism ( h ) is the side that runs vertical to the page and marked by H = 3 feet.
- So the dimensions of the larger rectangular prism are:
( L , W , H ) = ( 8 , 2 , 3 ) feet
b)
- The total amount of cement in cubic feet required to make two rectangular prism with dimensions evaluated above is the sum of smaller and larger rectangular prism volumes.
- The volume of a rectangular prism is given by:
V-prism = Length*width*height
- So the total volume V_t would be:
V_t = V_small + V _large
V_t = ( l*w*h ) + ( L*W*H )
V_t = ( 4*2*3 ) + ( 8*2*3 )
V_t = ( 4*2*3 ) + ( 8*2*3 )
V_t = ( 24 ) + ( 48 )
V_t = 72 ft^3
1.Disc method.
In this method the volume is given by:
![\boxed{V=\pi\int\limits_a^b\big[f(x)\big]^2}](https://tex.z-dn.net/?f=%5Cboxed%7BV%3D%5Cpi%5Cint%5Climits_a%5Eb%5Cbig%5Bf%28x%29%5Cbig%5D%5E2%7D)
so:
![V=\pi\int\limits_1^3x^4\,dx=\boxed{\pi\int\limits_1^3\big[x^2\big]^2\,dx}](https://tex.z-dn.net/?f=V%3D%5Cpi%5Cint%5Climits_1%5E3x%5E4%5C%2Cdx%3D%5Cboxed%7B%5Cpi%5Cint%5Climits_1%5E3%5Cbig%5Bx%5E2%5Cbig%5D%5E2%5C%2Cdx%7D)
A) Function
over the interval ![[1,3]](https://tex.z-dn.net/?f=%5B1%2C3%5D)
B) We use disk method and f(x) is function of variable x, so we <span>rotate the curve about the x-<span>axis.
2. Shell method.
In this case volume is given by:
</span></span>
So there will be:
A) Function
over the interval
B) We use shell method and f(x) is function of variable x, so we <span>rotate the curve about the y-<span>axis.</span></span>
In this method the volume is given by:
so:
A) Function
B) We use disk method and f(x) is function of variable x, so we <span>rotate the curve about the x-<span>axis.
2. Shell method.
In this case volume is given by:
</span></span>
So there will be:
A) Function
B) We use shell method and f(x) is function of variable x, so we <span>rotate the curve about the y-<span>axis.</span></span>