/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 89 What happens to the volume of a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 89

What happens to the volume of a sphere if its radius is doubled?

Short Answer

Expert verified
The volume of the sphere increases by a factor of 8 when the radius is doubled.

Step by step solution

01

Identifying the given and required values

The given value in this problem is that the radius of a sphere is doubled. The required value is how this action affects the volume of the sphere. The initial radius is \(r\) and the doubled radius is \(2r\). The volume with the initial radius is \(V = \frac{4}{3} \pi r^3\). We want to find the new volume when the radius is doubled.
02

Calculate the volume with the doubled radius

We will now substitute \(2r\) in the place of \(r\) in the volume formula. This yields \(V' = \frac{4}{3} \pi (2r)^3\) . This multiplies out to \(V' = \frac{4}{3} \pi 8r^3\), which simplifies to \(V' = 8 \times \frac{4}{3} \pi r^3\).
03

Compare the two volumes

We compare the volume of the sphere with radius \(r\) and the volume of the sphere with radius \(2r\). This comparison \(V' / V = 8 \times \frac{4}{3} \pi r^3 / \frac{4}{3} \pi r^3\) simplifies to \(V' / V = 8\). This means the volume of the sphere is multiplied by 8 when its radius is doubled.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I find that my answers involving \(\pi\) can vary slightly depending on whether I round \(\pi\) mid-calculation or use the \(\pi\) key on my calculator and then round at the very end.

A rectangular field is five times as long as it is wide. If the perimeter of the field is 288 yards, what are the field's dimensions?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. In an inequality such as \(5 x+4<8 x-5,\) I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.

A car rental agency charges 180 dollars per week plus 0.25 dollars per mile to rent a car. How many miles can you travel in one week for 395 dollars ?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Membership in a fitness club costs 500 dollars yearly plus 1 dollars per hour spent working out. A competing club charges 440 dollars yearly plus 1.75 dollars per hour for use of their equipment. How many hours must a person work out yearly to make membership in the first club cheaper than membership in the second club?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.