Test Index

TGTET Paper 1 Exam 23 Jul 2017 Paper

© examsnet.com
Question : 99 of 150
Marks: +1, -0
If each edge of a cube is doubled, then its volume becomes ______
Solution:  
Concept:
The volume of a cube is directly proportional to the cube of its side length.
Explanation:
Let's consider a cube with an initial side length. We can represent this initial side length using a variable.
Let the initial side length of the cube be ss.
The initial volume of the cube, VinitialV_{initial}, is given by the formula: Vinitial=s3V_{initial} = s^3.
Now, the problem states that each edge of the cube is doubled. So, the new side length becomes 2s2s.
The new volume of the cube, VnewV_{new}, will be: Vnew=(2s)3V_{new} = (2s)^3.
Calculating this, we get: Vnew=23×s3=8s3V_{new} = 2^3 \times s^3 = 8s^3.
To find out how many times the volume has increased, we compare the new volume to the initial volume:
Ratio of new volume to initial volume = VnewVinitial=8s3s3\frac{V_{new}}{V_{initial}} = \frac{8s^3}{s^3}.
Simplifying this ratio, we get 8s3s3=8\frac{8s^3}{s^3} = 8.
This means the new volume is 8 times the initial volume.
Answer:
8 times
© examsnet.com
Go to Question: