Question : Each side of a cube is decreased by 25%. Find the ratio of the volumes of the original cube and the resulting cube.
Option 1: 8 : 1
Option 2: 27 : 64
Option 3: 64 : 1
Option 4: 64 : 27

Question

Question : If a number is increased by 25% and the resulting number is decreased by 25%, then the percentage increase or decrease finally is:
Option 1: no change
Option 2: decreased by $6 \frac{1}{4}$ %
Option 3: increased by $6 \frac{1}{4}$ %
Option 4: increased by $6$ %

33 Views

Answer 1

Correct Answer: 64 : 27

Solution : If each side of a cube is decreased by 25%, the new side length = $a^{'} = a - 0.25 a = 0.75 a$
The volume of the new cube $= V^{'} = (a^{'})^{3} = (0.75 a)^{3}$
The ratio of the volumes of the original cube and the resulting cube,
⇒ $\frac{V}{V^{'}} = \frac{a^{3}}{(0.75 a)^{3}} = \frac{1}{{0.75}^{3}} = \frac{100 \times 100 \times 100}{75 \times 75 \times 75} = \frac{64}{27}$
Hence, the correct answer is 64 : 27.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Law Preparation

MBA Preparation

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Resources

Exams

Top Schools

Products & Resources

NCERT Study Material

Popular Searches

Question : Each side of a cube is decreased by 25%. Find the ratio of the volumes of the original cube and the resulting cube.Option 1: 8 : 1Option 2: 27 : 64Option 3: 64 : 1Option 4: 64 : 27

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CHSL

Download Careers360 App

All this at the convenience of your phone

Scan and download the app

Sign In/Sign Up

Question : Each side of a cube is decreased by 25%. Find the ratio of the volumes of the original cube and the resulting cube.
Option 1: 8 : 1
Option 2: 27 : 64
Option 3: 64 : 1
Option 4: 64 : 27