Question

A bookcase is 8 feet high, 1 foot deep, and 2 feet wide. How much space (in volume) does the bookcase take up?​

Answer 1

Answer:

The volume of the bookcase is 16 cubic feet.

Step-by-step explanation:

Hey there!

We are given three values (in feet) and asked to find the volume of a bookcase:

• 8 feet high
• 1 foot deep
• 2 feet wide

We want to find the volume. In order to do this, we need to define:

1. the formula for finding the volume of a rectangular prism
2. what values our data fits with

Therefore, the formula for volume is: $v = l \times w \times h$

• $v$ - volume
• $l$ - length
• $w$ - width
• $h$ - height

Finally, we need to assign each number value to either the length, the width, or the height.

Wide is a synonym for width, so our width is 2 feet.

Deep is another way of saying the space inside of the bookshelf, which would be the length (1 foot).

High would refer to how tall something is, so the height is 8 feet.

Now, let's plug in our values and solve for $v$.

• $v = l \times w \times h$
• $v = 1 \times 2 \times 8$
• $v = (1 \times 2) \times 8$
• $v = 2 \times 8$
• $v = \text{16 cubic feet}$

It's important to note that since we are finding volume, our measurement of feet becomes cubic feet.

Therefore, the volume of the bookcase is 16 cubic feet.

Answer 2

Digram:

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf A}\put(11.1,5.4){\bf B}\put(11.2,9){\bf C}\put(5.3,8.6){\bf D}\put(3.3,10.2){\bf E}\put(3.3,7){\bf F}\put(9.25,10.35){\bf H}\put(9.35,7.35){\bf G}\put(3.5,6.1){\sf 1\:foot}\put(7.7,6.3){\sf 2\:feet}\put(11.3,7.45){\sf 8\:feet}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

Given:

⇢ Length = 1 foot

⇢ width = 2 feet

⇢ height = 8 feet

To find:

⇢ Volume of the book case

Solution:

By seeing the dimensions we came to know that book case is in the shape of cuboid.

know as we know volume of cuboid is :-

$\bigstar \boxed{ \rm{}Volume \: of \: cuboid = length \times width \times height}$

By using this formula we can find value of volume of cuboid.

so:

$: \implies \sf{}Volume \: of \: cuboid = length \times width \times height$

$: \implies \sf{}Volume \: of \: cuboid = 1 \times 2 \times 8$

$: \implies \boxed{\frak{Volume \: of \: cuboid = 16} } \bigstar$

$\therefore \underline \textsf{volume of cuboid is \textbf{16 feet}}$

know more

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$