Question

Three ice cubes of equal side length 4 cm have the same volume as the rectangular prism of ice of dimensions given below. What should be the missing dimension of the rectangular prism?

• A. $6\text{cm}$
• B. $5\text{cm}$
• C. $8\text{cm}$
• D. $3\text{cm}$

Answer 1

The correct option is A $6\text{cm}$

Volume of cube $=\text{Side}\times \text{Side}\times \text{Side}=4\times 4\times 4=64\text{cu cm}$
Volume of 3 cubes $=3\times \text{Volume of a cube}=3\times 64=192\text{cu cm}$
Volume of the rectangular prism = Volume of 3 cube
Volume of the rectangular prism $=3\times \text{volume of a cube}$
Volume of the rectangular prism $=192\text{cu cm}$
Volume of the rectangular prism $=8\times 4\times h=192\text{cu cm}$
$32\text{sq cm}\times h\text{cm}=192\text{cu cm}$
$h\text{cm}=192\text{cu cm}÷32\text{sq cm}=6\text{cm}$