Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches (in). The volume of the dictionary will be
216in^(3). What must be the area of the front cover, a face perpendicular to the thickness, in square inches?

A new dictionary in the shape of a rectangular prism will have a thickness of $3$ inches (in). The volume of the dictionary will be $216 \mathrm{in}^{3}$ . What must be the area of the front cover, a face perpendicular to the thickness, in square inches?

View step-by-step help

View step-by-step help

Area and perimeter: word problems

Full solution

Q. A new dictionary in the shape of a rectangular prism will have a thickness of

3

inches (in). The volume of the dictionary will be

216 \mathrm{in}^{3}

. What must be the area of the front cover, a face perpendicular to the thickness, in square inches?

Understanding the relationship: Understand the relationship between volume, area, and thickness in a rectangular prism. $\newline$ The volume $V$ of a rectangular prism can be found by multiplying the area $A$ of the base (or front cover in this case) by the thickness $t$ of the prism. $\newline$ The formula is $V = A \times t$ .
Solving for the area: Given the volume and thickness, solve for the area of the front cover. $\newline$ We are given the volume $V = 216 \text{ in}^3$ and the thickness $t = 3 \text{ in}$ . $\newline$ Using the formula from Step $1$ , we can solve for $A$ : $\newline$ $A = \frac{V}{t}$ .
Calculating the area: Calculate the area of the front cover. $\newline$ Substitute the given values into the equation: $\newline$ $A = \frac{216 \text{ in}^3}{3 \text{ in}}.$ $\newline$ $A = 72 \text{ in}^2.$
Verifying the calculation: Verify the calculation to ensure there are no math errors. $\newline$ Double-check the division: $\newline$ $216$ divided by $3$ equals $72$ . $\newline$ No math errors are present in the calculation.

More problems from Area and perimeter: word problems

Question

A square window has a perimeter of \(136\) inches. How long is each side?

\newline

\_\_\_\_\_

Posted 2 months ago

Question

What is the greatest possible error for a measurement of

2

\newline

\_\_\_

Posted 3 months ago

Question

What is the percent error for a measurement of

5

?

\newline

If needed, round your answer to the nearest hundredth of a percent.

\newline

\newline

Posted 2 months ago

Question

Which measurement is more precise?

\newline

\newline

29.4

\newline

31

Posted 3 months ago

Question

Sako's garden is

6

yards long. What is the length of his garden in feet?

Posted 3 months ago

Question

Avery is designing a large rectangular sign. They want the sign to have an area of

2\,\text{m}^2

\frac{4}{5}\,\text{m}

. How tall should the sign be?

Posted 5 days ago

Question

Find the monthly payment for a

30

100000

4\%

Posted 3 months ago

Question

Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of

15 \frac{1}{2} \text{ m}^2

. Gabriel wants it to be

7 \frac{3}{4}

long. How wide does the planter box need to be?

Posted 3 months ago

Question

An electrician plans to install solar panels on a rectangular section of roof with an area of

180\text{m}^2

. This width of this section of roof is

7\frac{1}{5}

Posted 3 months ago

Question

Determine whether

\frac{3^{5m}}{3^{3m}}

is equivalent to each of the following expressions.

Posted 1 hour ago