Volumes Practice Test 1

Concept:The volume of a cuboid is the product of its length, breadth, and height; percentage increases change each dimension by a multiplying factor.Explanation:Let the original dimensions be $x$, $2x$, and $3x$.Original volume $V = x \times 2x \times 3x = 6x^3$.A $100\%$ increase makes a quantity $2$ times its original value.A $200\%$ increase makes a quantity $3$ times its original value.So the new dimensions become $2x$, $3(2x)=6x$, and $3(3x)=9x$.New volume $V' = 2x \times 6x \times 9x = 108x^3$.Increase in volume $= V' - V = 108x^3 - 6x^3 = 102x^3$.This increase compared to the original volume is $\frac{102x^3}{6x^3}=17$ times.Answer:The volume increases by $17$ times.