The length of a room is decreased by 10% and breadth is decreased by 20% while height is increased by 5% then what percentage change in the volume of the room?
Answers
Let l = 10 , b = 10 , h = 10
Volume = l*b*h
Volume = 10*10*10 = 1000
New l = 9 , b = 8 , h =10.5
New volume = 9*8*10.5 = 756
%change in volume = 1000 - 756
= 244 *100/1000
= 24.4
Step-by-step explanation:
Answer:
The length of a room is decreased by 10% and breadth is decreased by 20% while height is increased by 5% then the percentage change in the volume of the room is a decrease of 24.4%
Step-by-step explanation:
Let the length of the room be l, the breadth be b, and the height be h.
The changes in the measurements is given by:
Height = 1.05h
Length = 0.9l
Breadth = 0.80b
Now, the room is in form of a cuboid.
So, the volume is given by:
Volume = length × breadth × height
Original volume before the adjustments = lbh
The new volume after the changes = 0.9l × 0.80b × 1.05h = 0.756lbh
The change in volume = lbh - 0.756lbh = 0.244lbh
The percentage change in volume = 0.244lbh/lbh × 100% = 24.4%
The volume decreases by 24.4%