Question

The radius of a cone-shaped tank is 4 feet less than its height. If the height of the tank is (x - 3) feet, the expression below shows the volume of the tank.

1 over 3π(x - 7)2 (x - 3)

What does the factor π (x - 7)2 represent?

The total surface area of the tank

The area of the curved sides of the tank

The area of the circular base of the tank

The area of the base of about three such tanks

Answer 1

"height of the tank is (x - 3)" -> h = (x-3)

"radius of a cone-shaped tank is 4 feet less than its height." -> r = (x-3) - 4

\(\bf \textit{volume of a cone}=\cfrac{\pi {\color{red}{ r}}^2 {\color{blue}{ h}}}{3}\qquad r={\color{red}{ (x-3)-4}}\qquad h ={\color{blue}{ (x-3)}} \)

Answer 2

hmmm

Answer 3

So it would be C ?

Answer 4

well... not quite.... do you know what the area of a circle is?

Answer 5

3.14 right ?

Answer 6

pie...

Answer 7

\(\bf \textit{volume of a cone}=\cfrac{\pi {\color{red}{ r}}^2 {\color{blue}{ h}}}{3}\qquad r={\color{red}{ (x-3)-4}}\qquad h ={\color{blue}{ (x-3)}}
\\ \quad \\
\implies \textit{volume of this cone}=\cfrac{\pi {\color{red}{ [(x-3)-4]}}^2 {\color{blue}{ (x-3)}}}{3}
\\ \quad \\
\textit{keep in mind that }\textit{area of a circle }=\pi r^2\)

Answer 8

Ohhhh okay so it would be a the total surface area of the tank ?

Answer 9

is it?

Answer 10

Thats what makes the most sense to me...

Answer 11

well.. if you were to simplify (x-3) -4 what would you get?

Answer 12

I have no clue

Answer 13

wouldnt it be like 1x

Answer 14

you may want to review your linear simplification

Answer 15

(x-3) - 4 = x -3 - 4