Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A factory designs cylindrical cans
10cm in height to hold exactly
500cm^(3) of liquid. Which of the following best approximates the radius of these cans?
Choose 1 answer:
(A)
4cm
(B)
8cm
(C)
12.5cm
(D)
15.9cm

A factory designs cylindrical cans $10 \mathrm{~cm}$ in height to hold exactly $500 \mathrm{~cm}^{3}$ of liquid. Which of the following best approximates the radius of these cans? $\newline$ Choose $1$ answer: $\newline$ (A) $4 \mathrm{~cm}$ $\newline$ (B) $8 \mathrm{~cm}$ $\newline$ (C) $12.5 \mathrm{~cm}$ $\newline$ (D) $15.9 \mathrm{~cm}$

View step-by-step help

View step-by-step help

Scale drawings: word problems

Full solution

Q. A factory designs cylindrical cans

10 \mathrm{~cm}

in height to hold exactly

500 \mathrm{~cm}^{3}

of liquid. Which of the following best approximates the radius of these cans?

\newline

Choose

1

answer:

\newline

(A)

4 \mathrm{~cm}

\newline

(B)

8 \mathrm{~cm}

\newline

(C)

12.5 \mathrm{~cm}

\newline

(D)

15.9 \mathrm{~cm}

Volume Formula: To find the radius of the cylinder, we need to use the formula for the volume of a cylinder, which is $V = \pi r^2 h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height of the cylinder. We know the volume ( $V = 500 \text{ cm}^3$ ) and the height ( $h = 10 \text{ cm}$ ), so we can solve for $r$ .
Rearrange Formula: First, let's rearrange the formula to solve for $r$ . The formula for the volume of a cylinder is $V = \pi r^2 h$ . We can rearrange it to $r^2 = \frac{V}{(\pi h)}$ .
Plug in Values: Now, let's plug in the values we know: $V = 500 \, \text{cm}^3$ and $h = 10 \, \text{cm}$ . So, $r^2 = \frac{500}{(\pi \cdot 10)}$ .
Calculate: Calculating the right side of the equation gives us $r^2 = \frac{500}{(3.14159 \times 10)} \approx \frac{500}{31.4159} \approx 15.91549$ .
Find Radius: To find $r$ , we need to take the square root of both sides of the equation. So, $r \approx \sqrt{15.91549} \approx 3.989$ .
Final Approximation: The closest approximation to the radius of the can from the given options is $4\,\text{cm}$ , which is option $(A)$ .

More problems from Scale drawings: word problems

Question

A die is created by smoothing the corners of a plastic cube and carving indented pips. The original cube had an edge length of

2

(\mathrm{cm})

. The volume of the final die is

7.5 \mathrm{~cm}^{3}

. What is the volume of the waste generated by creating the die from the cube in

\mathrm{cm}^{3}

Posted 4 months ago

Question

We want to find the intersection points of the graphs given by the following system of equations:

\newline

\left\{\begin{array}{l} y=2 x-1 \\ x^{2}+y^{2}=1 \end{array}\right.

\newline

One of the intersection points is

(0,-1)

\newline

Find the other intersection point. Your answer must be exact.

Posted 8 months ago

Question

A(x)=(8+2 x)^{2}

\newline

Carmen wants to add a border around a square picture. The function shows the area of the picture in square inches if it has a border

x

inches wide. What are the dimensions of the picture without the border?

\newline

1

\newline

2

2

\newline

6

6

\newline

8

8

\newline

10

10

Posted 9 months ago

Question

s=-11.8(t-1.2)^{2}+17

\newline

The equation models the horizontal distance,

s

, in centimeters, of a particular image on a computer screen from the left-hand edge of the screen,

t

seconds after appearing. If the image moves in from the left-hand edge of the screen during an on-screen animation, how far to the right does the image travel?

\newline

1

\newline

1

2

\newline

5

2

\newline

17

\newline

34

Posted 9 months ago

Question

A soap company changes the design of its soap from a cone to a sphere. The cone had a height of

3

(\mathrm{cm})

and a radius of

2 \mathrm{~cm}

. The sphere has a diameter of

3 \mathrm{~cm}

. The new design contains

\frac{\pi}{f}

cubic centimeters more soap than the old design. What is the value of

f

Posted 7 months ago

Question

Mindy is a sculptor. She has a cylinder of stone with a radius of

3

(\mathrm{m})

and a height of

2 \mathrm{~m}

. She needs to carve out a sphere of radius

1 \mathrm{~m}

from the cylinder. Mindy must cut away

\frac{v}{3} \pi

\left(\mathrm{m}^{3}\right)

of stone from the cylinder in order to be left with the sphere. What is the value of

v

Posted 3 months ago

Question

A cylindrical soda can has a volume of

108 \pi

cubic centimeters

\left(\mathrm{cm}^{3}\right)

and a height of

12 \mathrm{~cm}

. What is the surface area of the soda can in square centimeters?

\newline

1

\newline

18 \pi \mathrm{cm}^{2}

\newline

36 \pi \mathrm{cm}^{2}

\newline

72 \pi \mathrm{cm}^{2}

\newline

90 \pi \mathrm{cm}^{2}

Posted 8 months ago

Question

\mathrm{Cleo}

are looking for a location to open their new yoga studio. A fellow studio owner suggests a location that will fit

28

756

square foot area. Assuming that each student has a spot

x

3

times as long, what is the length, in feet, of the space they are allotting to each student?

\newline

1

\newline

1

\newline

3

\newline

9

\newline

27

Posted 6 months ago

Question

Morgan is designing a rectangular quilt. The quilt will be

1 \frac{3}{5} \mathrm{~m}

wide and will have an area of

6 \mathrm{~m}^{2}

\newline

How long is the quilt?

\newline

Posted 8 months ago

Question

You pick a card at random, put it back, and then pick another card at random.

\newline

4

\newline

5

\newline

6

\newline

7

\newline

What is the probability of picking a number greater than

5

and then picking a

4

\newline

Write your answer as a percentage.

Posted 25 days ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant