Question

The dimensions of a cuboid is $10cm\times 8cm\times 5cm$. Calculate the volume of the new cuboid if the scale factor is $0.5$.

• A. 50

Answer 1

The correct option is A 50
Given:
Dimensions of the cuboid $=10cm\times 8cm\times 5cm$

Scale factor $=0.5$

There are two ways to calculate the volume of the new cuboid.

Method - $1$: Calculate the dimensions of the new cuboid

Dimensions of the new cuboid $=(10\times 0.5)cm\times (8\times 0.5)cm\times (5\times 0.5)cm$

$=5cm\times 4cm\times 2.5cm$

Volume $=5\times 4\times 2.5c{m}^3=50c{m}^3$

Method - $2$: Multiply the scale factor with the volume of the actual cuboid

Volume of the actual cuboid $=10\times 8\times 5c{m}^3$

$=400c{m}^3$

Volume of the new cuboid $=400\times 0.5\times 0.5\times 0.5c{m}^3$

The scale factor has been multiplied thrice because there are three dimensions and each dimension will be affected when the scale factor is multiplied.

$=50c{m}^3$