Ask question

Ask question

All categories

3 years ago

6

A lab technician made a 14 cm diameter hole through the middle of a cylinder that has a diameter of 20 cm and a height of 28 cm.

What is the approximate volume of the finished cylinder, to the nearest tenth of a centimeter

1 answer:

Step2247 [10]3 years ago

8 0

Answer:

The volume of the finished cylinder is $4486.2 m^3$

Step-by-step explanation:

To find the volume of the finished cylinder, we have to first find the volume of the hole (with 14 cm diameter and a height of 28 cm) and subtract it from the volume of the original cylinder (with diameter of 20 cm and a height of 28 cm).

Note: The hole is also cylindrical in shape.

The volume of a cylinder is given as:

$V = \pi r^2h$

where r = radius, h = height

VOLUME OF THE HOLE

The diameter of the hole is 14 cm, hence, its radius is 7 cm (14 / 2 = 7)

Its volume is:

$V = \pi *7^2 * 28\\V = 4310.3 m^3$

VOLUME OF THE ORIGINAL CYLINDER

The diameter of the cylinder is 20 cm, hence, its radius is 10 cm (20 / 2 = 10)

Its volume is:

$V = \pi *10^2 * 28\\V = 8796.5 m^3$

Hence, the volume of the finished cylinder will be:

$8796.5 - 4310.3 = 4486.2 m^3$

The volume of the finished cylinder is $4486.2 m^3$

You might be interested in

Points Pand Q lie in plane A. How many lines contain P

jeka94

Answer:

The correct answer is :

1. Line PQ (One line PQ).

Step-by-step explanation:

The first step to solve this question is to draw the plane A with the points P and Q lying on it.

We know that given two different points there is only one line that contains this two different points.

Let's analyze each option.

''2. Lines PQ and QP''

This option is wrong because there aren't two different lines. In fact it is only one line that can be named line PQ or line QP.

''3. The 2 lines PQ and QP plus another line that does not lie in plane A.''

This option is assuming that exist three lines that contain P and Q. This option is also wrong.

''1. Line PQ''

This option is correct. It will be clarify with the drawing I will attach.

''We can't name them all!''

This option is assuming that exist infinite lines that contain P and Q. This option is wrong.

In the drawing I call the line that contains P and Q as line L.

Given that P and Q lie in plane A necessarily the line L must lie on the plane A.

8 0

3 years ago

Plsss helpppppppppp if you do, you a cool guy or girl

STatiana [176]

9514 1404 393

Answer:

Tyler
2 hundredths of a mile

Step-by-step explanation:

The graph is a little difficult to read, but we note that there are 6 grid lines between times that are 2 minutes apart. So, each grid line stands for 2/6 = 1/3 minute.

At the 1-mile mark, the graph crosses 1 grid line above 8 minutes, indicating it takes Tyler 8 1/3 minutes to run 1 mile.

Then in 10 minutes, Tyler will run ...

distance = speed · time = 1 mile/(8 1/3 min) · 10 min

= 1/(25/3)·10 = 10·3/25 = 30/25 = 1.2 . . . . miles

__

The equation tells you that Elena runs each mile in 8.5 minutes. To see how far she runs in 10 minutes, we can solve ...

10 = 8.5x

x = 10/8.5 ≈ 1.18 . . . . miles

So, Tyler runs farther in 10 minutes by a distance of ...

1.20 -1.18 = 0.02 . . . . miles

8 0

3 years ago

yasmine wants to swim 50 miles . She plans to swim 1/4 mile each day. How many days will it take her to swim 50 miles?

Sav [38]

50 divide by .25 = 200 days

8 0

3 years ago

a total of 695 tickets were sold for the school play. They were either adult or student tickets. There was 55 fewer students tic

FinnZ [79.3K]

Answer:

375 + 320

Step-by-step explanation:

375 adult

320 students

equals 395

4 0

2 years ago

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

3 years ago