Question

John built a rectangular cardboard box $25$ cm high with a square base and a volume of $2,500$ ${cm}^3$. Then he realized he did not need a box that large, so he chopped off the height of the box reducing its volume to $1,000$ ${cm}^3$. Was the new box cubical? Also, state its' height.

• A. $20cm$
• B. $10cm$
• C. $30cm$
• D. $40cm$

Answer 1

The correct option is B $10cm$

Volume $=$ $($Length $\times$ Breadth$)$ $\times$ Height
$=$ Base area $\times$ height
Base area $=$ $\frac{2500}{25}=100{cm}^2$
Length $\times$ Length $=$ $100{cm}^2$
Length $=$ $\sqrt{\left(100\right)}=10$ cm
Now, $1000=10\times 10\times$ new heigth
New height $=\frac{1000}{(10\times 10)}=\frac{1000}{100}=10$ cm
Yes, the new box was cubical (as length, width and height are all same).