Question

A box is to be constructed by cutting out equal squares from the corners of a 30-cm square piece of cardboard and turning up the sides.

a. write a function v(x) for the volume of the box
b. for what value of x will the volume of the box equal 1568 cubic centimeters?
c. what will be the volume of the box if x = 6 centimeters?

Answer 1

Answer:

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Answer 2

Tip:

• Volume of rectangle $=length\times width\times height$

Explanation:

• Given that a box is constructed by cutting out equal squares from a $30~cm$ square piece.
• We have to find the Volume of the box, and the values of $x$ for which the volume will be $1568~cm^3$ and the volume if $x=6~cm$.

Step

Step 1 of 3:

The height of the box is $x$,

The sides of the base of the box is $30-2x$.

Hence,

Volume $=(30-2x)^2\times x$

So, $V(x)=(30-2x)^2x$

Step 2 of 3:

When $V=1568$

Then, $(30-2x)^2x=1568$

By solving this we get the values of $x$ as

$x=2.5,~x=8,~x=18.5$

Step 3 of 3:

When $x=6~cm$, then

$V(6)=((30-2(6))^2)6\\~~~~~~~=((30-12)^2)6\\~~~~~~~=(18^2)6\\~~~~~~~=1844$