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 (x - 3) represent?

The area of the base of the tank

The area of the curved sides of the tank

The volume of 3 of the same cone-shaped tanks

The volume of 6 of the same cone-shaped tanks

Answer 1

@AllTehMaffs

Answer 2

hi hi - what's your thought? ^^

Answer 3

I have no idea

Answer 4

My guess would be A

Answer 5

if

\[V= \frac{1}{3}\pi(x-7)^2(x-3) =\ \text{Volume of one cone}\]
then
\[ \pi(x-7)^2(x-3) = 3 \Big(\frac{1}{3}\pi(x-7)^2(x-3) \Big) = 3V= \ \text{Volume of ? cones}\]

Answer 6

3

Answer 7

yah ^_^

Answer 8

So the answer would be C! Do you know where those expressions they used came from?

Answer 9

No

Answer 10

The volume of a cone is
\[V_{cone}= \frac{1}{3} BH\]
Its base is the area of a circle
\[ B=\pi R^2\]
and its height is just H. So in this problem, the height was given by
\[H=(x-3)ft\]
and the radius of the base was "4 feet less than the height"
\[R=H-4ft = (x-3)ft-4ft = (x-7) ft\]

So the volume expression that they gave would be
\[V_{cone}= \frac{1}{3} (B)(H) =\frac{1}{3} (\pi R^2)(H) = \frac{1}{3} \Big(\pi(x-7)^2\Big)\Big(x-3\Big)ft^3\]