Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many times smaller is the volume of a cylinder if the diameter is multiplied by $\frac{1}{2}$ ?

View step-by-step help

View step-by-step help

Solve proportions: word problems

Full solution

Q. How many times smaller is the volume of a cylinder if the diameter is multiplied by

\frac{1}{2}

?

Volume Formula: The volume of a cylinder is given by the formula $V = \pi r^2 h$ , where $r$ is the radius and $h$ is the height of the cylinder.
Halving Diameter: If the diameter is halved, then the new diameter is $d/2$ , and the new radius is $r/2$ , since the radius is half of the diameter.
Volume Comparison: We need to compare the volume of the original cylinder with the volume of the new cylinder with the halved diameter. Let's call the original volume $V_1$ and the new volume $V_2$ .
Original Volume: The original volume $V_1$ is $\pi r^2 h$ .
New Volume Calculation: The new volume $V_2$ , with the halved diameter (and thus halved radius), is $\pi(\frac{r}{2})^2h = \pi(\frac{r^2}{4})h = (\frac{1}{4})\pi r^2h$ .
Volume Ratio Calculation: To find out how many times smaller the new volume is compared to the original volume, we divide $V_1$ by $V_2$ : $\frac{V_1}{V_2} = \frac{\pi r^2 h}{(\frac{1}{4})\pi r^2 h}$ .
Simplified Ratio: Simplify the expression: $V_1/V_2 = (\pi r^2 h) / ((1/4)\pi r^2 h) = 4/1 = 4$ .
Final Conclusion: The new volume is $4$ times smaller than the original volume when the diameter of the cylinder is halved.

More problems from Solve proportions: word problems

Question

Recently, frogs have been disappearing from the wild due to a contagious fungus. To monitor the current population in a certain region, Alan collects

28

frogs, marks them, and releases them. Later, he collects

110

frogs and finds that

11

of them are marked. To the nearest whole number, what is the best estimate for the frog population?

\_\_\_\_

Posted 3 months ago

Question

v

in the proportion.

\frac{v}{6} = \frac{25}{30}

v =

Posted 3 months ago

Question

\newline

\frac{7}{3}x= 21

\newline

x =

Posted 4 months ago

Question

Fabio and Carlos play on a basketball team together. In the last game, Fabio had

7

points less than

2

times as many points as Carlos. Fabio scored

31

points in the game. How many points did Carlos score in the last game?

Posted 2 months ago

Question

Stephanie is twice as old as her sister Rosa. If Stephanie is

\mathbf{1 8}

years old, how old is Rosa?

Posted 1 month ago

Question

Yohan is blowing up a spherical balloon. He blows

108 \pi

cubic centimeters of air with every breath. It takes him

72

breaths to fully inflate the balloon. What is the radius of the balloon in centimeters when it is fully inflated?

Posted 2 months ago

Question

4

gallons of gas in her car. If the fuel efficiency of her car is

23

miles per gallon, how many miles can Nadine drive before running out of gas?

Posted 2 months ago

Question

According to a website where users review their doctors,

116

119

users would recommend Dr. Gutierrez to their friends and family. If the website users are representative of Dr. Gutierrez's

1

293

patients, about how many patients would recommend Dr. Gutierrez to their friends and family?

\newline

(Round your answer to the nearest whole number.)

Posted 4 months ago

Question

12

chicken wings in

3

minutes. She eats the chicken wings at a constant rate.

\newline

How many chicken wings can Bao eat in

12

\newline

Posted 4 months ago

Question

The double number lines show the ratio of cups to gallons.

\newline

How many cups are in

3

\newline

Posted 4 months ago