if the length of a room is decreased by 10 persant and the breadth is decreased by 20%, while height is increase by 5%, then what % change in the volume of the room
Answers
Answer:
New volume decreases by 24.4%
Step-by-step explanation:
Let the original dimensions of the room be:
L = original length
B = original breadth
H = original height
V = original volume = L*B*H
After the changes, we have:
new length = 0.9*L [10% decrease => 90% of original => 0.9 of original]
new breadth = 0,8*B
new height = 1.05*H
New volume = new length * new breadth * new height
= 0.9*L * 0.8*B * 1.05*H
= (09*0.8*1.05)*(L*B*H)
= (0.756)*V
New volume = (0.756)*V
= (1 - 0.244)*V
= V - 0.244*V
= V - (24.4/100)*V
= V - 24.4% of V
= Original Volume - 24.4% of Original Volume
=> New Volume is 24.4% lower than original volume
=> New volume decreases by 24.4%
Answer:
The percentage change in the volume of the room is 24.4%
Step-by-step explanation:
Let the original length of the room be L, the breadth W, and height H.
The new measurements are given by:
Length = 0.9 L
Breadth = 0.8 W
Height = 1.05 H
The original volume of the room = LWH
The new volume of the room is given by: (0.9L × 0.8W × 1.05H) = 0.756 LWH
The change in volume is given by : LWH - 0.756LWH = 0.244 LWH
The percentage change is given by: 0.244/1 × 100 = 24.4%