Volume of a Orthohedron: Using variables

The the area of the rectangle DBFH is 20 cm².

Work out the volume of the cuboid ABCDEFGH.

We know the area of DBHF and also the length of HF

We will substitute into the formula in order to find BF, let's call the side BF as X:

$4\times x=20$

We'll divide both sides by 4:

$x=5$

Therefore, BF equals 5

Now we can calculate the volume of the box:

$8\times4\times5=32\times5=160$

$160$ cm³

Rectangle ABCD has an area of 12 cm².

Calculate the volume of the cuboid ABCDEFGH.

Based on the given data, we can argue that:

$BD=HF=2$

We know the area of ABCD and also the length of DB

We'll substitute in the formula to find CD, let's call the side CD as X:

$2\times x=12$

We'll divide both sides by 2:

$x=6$

Therefore, CD equals 6

Now we can calculate the volume of the box:

$6\times2\times3=12\times3=36$

$36$

A building is 21 meters high, 15 meters long, and 14+30X meters wide.

Express its volume in terms of X.

We use a formula to calculate the volume: height times width times length.

We rewrite the exercise using the existing data:

$21\times(14+30x)\times15=$

We use the distributive property to simplify the parentheses.

We multiply 21 by each of the terms in parentheses:

$(21\times14+21\times30x)\times15=$

We solve the multiplication exercise in parentheses:

$(294+630x)\times15=$

We use the distributive property again.

We multiply 15 by each of the terms in parentheses:

$294\times15+630x\times15=$

We solve each of the exercises in parentheses to find the volume:

$4,410+9,450x$

$4410+9450x$

Given an cuboid whose width is equal to X

The length is greater by 4 of its width

The height of the cuboid is equal to 2 cm

The volume of the cuboid is equal to 16X

Calculate the width of the cuboid (X)

2 cm

Look at the cuboid of the figure:

The volume of the cuboid is

60 cm³.

Work out the value of X.

$2$

The volume of the cuboid in the figure is 75 cm³.

Calculate the value of X.

Impossible to know.

Look at the cuboid in the figure below.

The volume of the cuboid is 80 cm³.

Calculate X.

$2$

Look at the following cuboid.

The volume of the cuboid is 60 cm³.

What is the length of the side HF?

$3$

Look at the following cuboid.

Express the volume of the cuboid in terms of X.

$7x^2+63x+140$

A rectangular prism has a square base (X).

Its edge is 5 times longer than the side of the base.

Choose the correct expression.

X^2(X+5)

In an cuboid with a square base, the cuboid edge
It is greater by 5 of the base side.
We mark the side of the base with X,

What is true?

$V=X^2(X+5)$

Look at the rectangular prism below.

The area of rectangle CAEG is 15 cm².

The area of rectangle ABFE is 24 cm².

Calculate the volume of the rectangular prism ABCDEFGH.

$120$