Given:
The radius, r=4x
The height,
![h=21xy^2](https://tex.z-dn.net/?f=h%3D21xy%5E2)
To find the volume of the cone:
The volume of the cone formula is,
![V=\frac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
Substitute the values of r and h in the above formula we get,
![\begin{gathered} V=\frac{1}{3}\pi\times(4x)^2\times21xy^2 \\ =\frac{1}{3}\pi\times16x^2\times21xy^2 \\ =\pi\times16x^2\times7xy^2 \\ =112\pi x^3y^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes%284x%29%5E2%5Ctimes21xy%5E2%20%5C%5C%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes16x%5E2%5Ctimes21xy%5E2%20%5C%5C%20%3D%5Cpi%5Ctimes16x%5E2%5Ctimes7xy%5E2%20%5C%5C%20%3D112%5Cpi%20x%5E3y%5E2%20%5Cend%7Bgathered%7D)
Hence, the volume of the cone is
![V=112\pi x^3y^2](https://tex.z-dn.net/?f=V%3D112%5Cpi%20x%5E3y%5E2)
Thus, the correct option is option D.
Answer:
58 degrees
Step-by-step explanation:
90+32+58=180
all triangles equal a total of 180 degrees hope this helps
The
<u>correct answer</u> is:
Matthew's rate is higher by $50 per month.
Explanation:
We know that Christopher's rate is $550 per month.
To find Matthew's rate, we will treat the data we have as ordered pairs:
(3, 1800)
(6, 3600)
(9, 5400)
We find the slope of the line between these points. The formula for slope is:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Using the first two points, we have:
![m=\frac{3600-1800}{6-3}=\frac{1800}{3}=600](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3600-1800%7D%7B6-3%7D%3D%5Cfrac%7B1800%7D%7B3%7D%3D600)
To verify Matthew saves the same amount each month, we will find the slope between the second two points and make sure they're the same:
![m=\frac{5400-3600}{9-6}=\frac{1800}{3}=600](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5400-3600%7D%7B9-6%7D%3D%5Cfrac%7B1800%7D%7B3%7D%3D600)
Matthew's rate is $600 per month.
This is higher than Christopher's by 600-550=$50 per month.
320 cubic inches
128 cubic inches
448 cubic inches
Step-by-step explanation:
Step 1:
Given,
Dimensions of the first rectangular prism = l * b * h = 16*5*4
[length is 16 as the total length is 20 and the width of the 2nd prism till the dotted line is 4]
Dimensions of the second rectangular prism = l * b * h = 4*4*8
We need to determine volume of the 2 prisms and the whole figure. The volume of rectangular prism can be obtained by multiplying the length breadth and the height.
Step 2:
Volume of the first prism = l * b * h = 16*5*4 = 320 cubic inches
Volume of the first prism = l * b * h = 4*4*8 = 128 cubic inches
The volume of the whole figure is the sum of the 2 rectangular prisms = 320 + 128 = 448 cubic inches