Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

As a birthday gift, Lauren received a new monogrammed suitcase to take on the family trip to Ireland. The suitcase is shaped like a rectangular prism. It is $10$ inches deep and $20$ inches tall. The suitcase contains $2,600$ cubic inches of packing space. $\newline$ Which equation can you use to find the width of the suitcase, $w$ ? $\newline$ Choices: $\newline$ (A) $10 \times 20 \times 2,600 = w$ $\newline$ (B) $10 \times w \times 20 = 2,600$ $\newline$ What is the width of the suitcase? $\newline$ Write your answer as a whole number or decimal. Do not round. $\newline$ ____ inches $\newline$

View step-by-step help

View step-by-step help

Volume of cubes and rectangular prisms: word problems

Full solution

Q. As a birthday gift, Lauren received a new monogrammed suitcase to take on the family trip to Ireland. The suitcase is shaped like a rectangular prism. It is

10

inches deep and

20

inches tall. The suitcase contains

2,600

cubic inches of packing space.

\newline

Which equation can you use to find the width of the suitcase,

w

?

\newline

Choices:

\newline

(A)

10 \times 20 \times 2,600 = w

\newline

(B)

10 \times w \times 20 = 2,600

\newline

What is the width of the suitcase?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

____ inches

\newline

Understand problem, identify equation: Step $1$ : Understand the problem and identify the correct equation to use. $\newline$ The suitcase is a rectangular prism with a volume of $2,600$ cubic inches. It has a depth of $10$ inches and a height of $20$ inches. We need to find the width, $w$ . The correct equation to represent the volume of a rectangular prism is $\text{length} \times \text{width} \times \text{height} = \text{volume}$ . Therefore, the equation to find the width is $10 \times w \times 20 = 2,600$ .
Solve equation for $w$ : Step $2$ : Solve the equation for $w$ . Using the equation $10 \times w \times 20 = 2,600$ , simplify it to find $w$ . $10 \times 20 \times w = 2,600$ $200 \times w = 2,600$ $w = \frac{2,600}{200}$ $w = 13$

More problems from Volume of cubes and rectangular prisms: word problems

Question

A cylindrical soda can has a volume of

108\pi\ \text{cm}^{3}

and a height of

12\text{cm}

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

\newline

1

\newline

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

\newline

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

\newline

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

\newline

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

Posted 8 months ago

Question

A cake pan is in the shape of a right rectangular prism

20\,\text{cm}

20\,\text{cm}

5\,\text{cm}

high. The pan contains

1,000\,\text{cm}^3

of batter. Approximately how far is the cake batter from the top of the pan?

\newline

1

\newline

1\,\text{cm}

\newline

2.5\,\text{cm}

\newline

5\,\text{cm}

\newline

7\,\text{cm}

Posted 8 months ago

Question

A contractor is to build a new structure at a farm for seed storage. It will have a rectangular base, which is

20

35

feet long, with walls of thickness

t

feet. The structure is

90

feet tall. Excluding the volume of the walls, which of the following functions best models the volume,

V

, in cubic feet, inside the structure?

Posted 7 months ago

Question

Rocio drops a ball from a height of

4

meters. Rocio observes that each time the ball bounces, it reaches a peak height which is

\newline

79\%

of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height,

\newline

h

, in meters, after

\newline

b

\newline

1

\newline

\newline

h=4\cdot0.79^{(b-1)}

\newline

\newline

h=4\cdot0.79^{b}

\newline

\newline

h=4-0.79\cdot b^{2}

\newline

\newline

h=4\cdot(1-0.79\cdot b^{2})

Posted 8 months ago

Question

Imani's grandmother's house is

5

miles west of her own house down Main Street. While at her grandmother's, Imani decides to ride her bike farther west down Main Street at

10

miles per hour. Which equation best describes the distance,

\newline

d

, in miles, Imani is from home after

\newline

t

\newline

1

\newline

d=5+10t

\newline

d=5-10t

\newline

d=5t+10

\newline

d=5t-10

Posted 8 months ago

Question

A piece of wood has a mass of

m_1

grams and a volume of

V_1

cubic centimeters. A second piece of wood has the same density

\rho

and a volume of

V_2

. What is the mass, in grams, of the second piece of wood?

Posted 8 months ago

Question

The function models

R

, the revenue, in dollars, from selling a particular board game at a price of

x

dollars. What is the revenue if the board game is sold at a price of

30

\newline

1

\newline

\$500,000

\newline

\$800,000

\newline

\$900,000

\newline

\$1,770,000

Posted 8 months ago

Question

Rocio drops a ball from a height of

4

meters. Rocio observes that each time the ball bounces, it reaches a peak height which is

79\%

of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height,

h

, in meters, after

b

\newline

1

\newline

h=4\cdot0.79^{(b-1)}

\newline

h=4\cdot0.79^{b}

\newline

h=4-0.79\cdot b^{2}

\newline

h=4\cdot(1-0.79\cdot b^{2})

Posted 8 months ago

Question

What is the volume, in cubic inches, of a rectangular prism with a height of

7

inches, a width of

5

inches, and a length of

5

\newline

V=\square

^{3}

Posted 8 months ago

Question

A rectangular prism has a length of

2

inches, a height of

16

inches, and a width of

15

inches. What is its volume, in cubic inches?

\newline

V=\square

^{3}

Posted 8 months ago

Related topics

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