Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

(1) A solid with volume 8 cubic units is dilated by a scale factor of
k to obtain a solid with volume
V cubic units. Find the value of
k which results in an image with each given volume.
PART A
216 cubic units
PART B
1 cubic unit
PART C
1,000 cubic units

( $1$ ) A solid with volume $8$ cubic units is dilated by a scale factor of $k$ to obtain a solid with volume $V$ cubic units. Find the value of $k$ which results in an image with each given volume. $\newline$ PART A $\newline$ $216$ cubic units $\newline$ PART B $\newline$ $1$ cubic unit $\newline$ PART C $\newline$ $1$ , $000$ cubic units

View step-by-step help

View step-by-step help

Scale drawings: word problems

Full solution

Q. (

1

) A solid with volume

8

cubic units is dilated by a scale factor of

k

to obtain a solid with volume

V

cubic units. Find the value of

k

which results in an image with each given volume.

\newline

PART A

\newline

216

cubic units

\newline

PART B

\newline

1

cubic unit

\newline

PART C

\newline

1

,

000

cubic units

Find Scale Factor for PART A: $\newline$ Find the scale factor $k$ for PART A where the final volume $V$ is $216$ cubic units. $\newline$ Use the formula for the scale factor in volume: $V = k^3 \times \text{original volume}$ . $\newline$ So, $k^3 = V / \text{original volume} = 216 / 8$ . $\newline$ $k^3 = 27$ . $\newline$ Now find the cube root of $27$ to get $k$ . $\newline$ $k = 3$ .
Find Scale Factor for PART B: $\newline$ Find the scale factor $k$ for PART B where the final volume $V$ is $1$ cubic unit. $\newline$ Again, use the formula: $V = k^3 \times \text{original volume}$ . $\newline$ $k^3 = V / \text{original volume} = 1 / 8$ . $\newline$ $k^3 = 1/8$ . $\newline$ Now find the cube root of $1/8$ to get $k$ . $\newline$ $k = 1/2$ .
Find Scale Factor for PART C: $\newline$ Find the scale factor $k$ for PART C where the final volume $V$ is $1,000$ cubic units. $\newline$ Use the formula: $V = k^3 \times \text{original volume}$ . $\newline$ $k^3 = V / \text{original volume} = 1000 / 8$ . $\newline$ $k^3 = 125$ . $\newline$ Now find the cube root of $125$ to get $k$ . $\newline$ $k = 5$ .

More problems from Scale drawings: word problems

Question

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

1

\newline

4 \mathrm{~cm}

\newline

8 \mathrm{~cm}

\newline

12.5 \mathrm{~cm}

\newline

15.9 \mathrm{~cm}

Posted 1 month ago

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 10 days 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 2 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 4 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 4 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 25 days 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 28 days 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 2 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 19 days 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 2 months ago