Ask question

Ask question

All categories

2 years ago

6

An ash borer is an invasive pest whose larvae eat the pulp of ash trees as they mature. A park ranger has a tree that is infeste

d with ash borers. She estimates they have eaten approximately 40% of the tree's pulp. If the ash tree's trunk has a radius of 2 feet and a height of 15 feet, what was the total volume of the tree trunk before the ash borers started eating it?

1 answer:

Ray Of Light [21]2 years ago

3 0

Answer:

$188.6$ cubic feet

Step-by-step explanation:

Let r, h denotes radius and height of the tree's trunk.

Radius of the tree's trunk = 2 feets

Height of the tree's trunk = 15 feets

The tree's trunk is in the shape of a cylinder.

Volume of cylinder (tree's trunk) $=\pi r^2h$

Put $r=2\,,\,h=15$

Volume of the tree's trunk $=\pi (2)^2(15)=60\pi$ cubic feet

Put $\pi=\frac{22}{7}$

So,

Volume of the tree's trunk $=60(\frac{22}{7})=\frac{1320}{7}=188.6$ cubic feet

You might be interested in

Find the volume of a right circular cone that has a height of 12.5 cm and a base with a circumference of 5.8 cm. Round your answ

BaLLatris [955]

Answer:

$V = 11.2 cm^3$

Step-by-step explanation:

Given

Shape: Right Circular cone

Height, h = 12.5 cm

Base circumference, C = 5.8cm

Required:

Calculate Volume

The volume of a cone is calculated as thus;

Volume, $V = \frac{1}{3}\pi r^2h$

Where V, r and h represent the volume, the radius and the height of the cone respectively

But first we need to calculate the radius of the cone.

Using formula of circumference.

$C = 2\pi r$

We have C to be 5.8cm

By substituting this value;

$5.8 = 2\pi r$

Divide through by $2\pi$

$\frac{5.8}{2\pi} = \frac{2\pi r}{2\pi}$

$r = \frac{5.8}{2\pi}$

$r = \frac{2.9}{\pi}$

Now, we can calculate the volume of the cone

By substituting $r = \frac{2.9}{\pi}$ and h = 12.5 cm;

$V = \frac{1}{3}\pi r^2h$ becomes

$V = \frac{1}{3}\pi * (\frac{2.9}{\pi})^2 * 12.5$

$V = \frac{1}{3}\pi * \frac{8.41}{\pi^2} * 12.5$

$V = \frac{1}{3} * \frac{8.41}{\pi} * 12.5$

Take $\pi$ as 3.14

$V = \frac{1}{3} * \frac{8.41}{3.14} * 12.5$

$V = 11.15976$

$V = 11.2 cm^3$ ---- Approximated

Hence, the volume of the cone is; $V = 11.2 cm^3$

4 0

2 years ago

If $9x^2 - 16x + k$ is a perfect square trinomial, find $k$.

Lady_Fox [76]

Answer:is this a real quistion

Step-by-step explanation:?

7 0

2 years ago

The back of Monique’s property is a creek. Monique would like to enclose a rectangular area, using the creek as one side and fen

gogolik [260]

Answer:

4050 sq. feet.

Step-by-step explanation:

Fencing is done on three sides of the rectangular area.

Given that there are 180 feet of fence available.

Then 2L + W = 180 ........(1), where L = length and W = width, of the rectangular plot.

Now, the area of the plot is given by A = LW

Now, from equation (1), we ger A = L (180 - 2L) ..... (2)

Then differentiating with respect to L in the both sides we get,

$\frac{dA}{dL} = 180 - 4L =0$ {Since condition for Area to be maximum is $\frac{dA}{dL}=0$ }

⇒ L = 45 feet.

Now, from equation (2), we have $A_{max} =L(180-2L) = 45(180 - 90) =4050$ square feet.

3 0

2 years ago

The figure below shows a line graph and two shaded triangles that are similar:Which statement about the slope of the line is tru

zzz [600]

Here is something to keep in mind.
when there is a downward slope, the slope will ALWAYS have a negative slope. even if it is above the x-axis. negative slopes will tend to go from positive y-axis to negative y-axis
so personally would have to go with -4
because the x-axis is by 4 each time. and this slope is going downward.

your answer will be D

6 0

2 years ago

Read 2 more answers

What fraction of 30 is 12

zloy xaker [14]

Call the mystery fraction ' F ' (for 'fraction').

12 is the mystery fraction of 30 .

12 = F x 30

Divide each side by 30 : F = 12/30 = 2/5 .

5 0

2 years ago