Question

An architect is redesigning a rectangular room on the blueprints of the house. He decides to double the width of the room, increase the length by 48 %, and increase the height by 18 %. By what factor has the volume of the room increased

Answer 1

Answer:

3.4928.

Step-by-step explanation:

Initial volume of the rectangular room = Length * Width * Height

V = LWH .............1

If the width is doubled then new width W2 = 2W

If the length is increased by 48%, the new Length L2 = L + 0.48L = 1.48L

If the height is increased by 18%, the new height H2 = H + 0.18H = 1.18H

The new volume after increasing all the dimensions will be;

V2 = L2W2H2

V2 = (1.48L)(2W)(1.18H)

V2 = 3.4928LWH ................2

Now we will divide equation 2 by 1 to have;

V2/V = 3.4928LWH/LWH

V2/V = 3.4928

V2 = 3.4928V

This means that the volume of the room has increased by the factor of 3.4928.