Length, Breadth and Height of a 3D figure is in the ratio 3:2:1. If the length is doubled and Breadth & Height are halved, then what is the % decrease in the volume of the solid?Decreased by 15%Decreased by 18%Decreased by 30%Decreased by 50%
Question
Length, Breadth and Height of a 3D figure is in the ratio 3:2:1. If the length is doubled and Breadth & Height are halved, then what is the % decrease in the volume of the solid?Decreased by 15%Decreased by 18%Decreased by 30%Decreased by 50%
Solution
The volume of a 3D figure (like a cuboid) is given by the formula: Volume = Length * Breadth * Height.
Initially, let's assume the Length = 3x, Breadth = 2x, and Height = 1x for some constant x. So, the initial volume = 3x * 2x * 1x = 6x^3.
According to the problem, the length is doubled and the breadth and height are halved. So, the new dimensions are: Length = 2 * 3x = 6x, Breadth = 2x/2 = x, and Height = 1x/2 = 0.5x. So, the new volume = 6x * x * 0.5x = 3x^3.
The percentage decrease in the volume = [(Initial Volume - New Volume) / Initial Volume] * 100 = [(6x^3 - 3x^3) / 6x^3] * 100 = 50%.
So, the volume of the solid has decreased by 50%.
Similar Questions
Length, Breadth and Height of a 3D figure is in the ratio 3:2:1. If the length is doubled and Breadth & Height are halved, then what is the % decrease in the volume of the solid?Decreased by 15%Decreased by 18%Decreased by 30%Decreased by 50%
Three-dimensional figures are typically measured by their _____, _____, and _____.A.weightB.heightC.widthD.altitudeE.length
Which statement about calculating the volume of a three-dimensional figure is TRUE?The volume of a three-dimensional figure is always less than its surface area.To determine volume, you multiply the surface area of the net by the height of the figure.The volume of a three-dimensional figure is always less than the area of the base.To determine volume, you calculate the area of the base and then multiply that product by the height of the figure.
Two-dimensional figures are typically measured by their _____ and _____.A.massB.widthC.volumeD.heightE.length
Two cuboids have the same volume. Their length are in the ratio 5 : 4 and their breadth are in the ratio 2 : 3. Find the ratio of their heights.Options5 : 66 : 54 : 55 : 4
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.