An Open Box with Volume Of $8000$ Cm $3$ Is to Be Constructed by Taking a Piece of Cardboard

question 67

Essay

An open box with volume of $8000$ cm $3$ is to be constructed by taking a piece of cardboard $40$ cm by $60$ cm, cutting squares of side length $x$ cm from each corner. Show that this can be done in two ways, and find the exact dimensions of the box in each case.

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Definitions:

U.S. Treasury Bonds

Long-term government debt securities issued by the United States Department of the Treasury with maturity periods over 20 years, offering a fixed interest rate.

Coupon Rate

The coupon rate is the annual interest payment made to bondholders, expressed as a percentage of the bond's face value.

Par Value

The nominal or face value of a bond, share of stock, or coupon as stated by the issuer; it is often a minimal amount like $0.01 or $1.00.

Matures

The point in time when a financial obligation, such as a bond or loan, reaches its due date and the principal amount must be repaid to investors or creditors.