Question

A rectangular prism-shaped room has dimensions $11$ ft $12$ ft $10$ ft. What will be the percentage decrease in the volume of the room if the height is reduced by $1.5$ ft?

• A. $20$%
• B. $1.5$%
• C. $15$%
• D. $12$%

Answer 1

The correct option is C $15$%

The room is in the shape of a rectangular prism.
Volume of the room, $V_1=(11\times 12)\times 10$
New height $=$ Original height $-1.5$ ft
$=10-1.5$
$=8.5$ ft

New volume of the room, $V_2=(11\times 12)\times 8.5$
Decrease in volume $=V_1-V_2$
$=(11\times 12)\times 10-(11\times 12)\times 8.5$
$=(11\times 12)\times (10-8.5)$
$=(11\times 12)\times 1.5$

Percentage decrease $=\frac{V_1-V_2}{V_1}\times 100$%

$=\frac{11\times 12\times 1.5}{11\times 12\times 10}\times 100$%

$=15$%

So, the volume of the room reduces by $15$% when its height is reduced by $1.5$ ft.