Chapter 5: Q. 71 (page 258)

The volume $V$ of a right circular cylinder of height $h$ and radius $r$ is $V = {πr}^{2} h .$ If the height is twice the radius, express the volume $V$ as a function of $r$ .

Short Answer

Expert verified

The volume, $V (r) = 2 {πr}^{3} .$

Step by step solution

Step 1. Given Information

Given that $V = {πr}^{2} h$ and $h (r) = 2 r .$

Step 2. Solution

We have to find $V$ as a function of $r$ .

Here, $V = {πr}^{2} h; h (r) = 2 r .$

Now,

$V \circ h (r) = V (h (r)) V \circ h (r) = {πr}^{2} {h (r)} V \circ h (r) = {πr}^{2} (2 r) V \circ h (r) = 2 {πr}^{3} V (r) = 2 {πr}^{3} .$

Step 3. Final Answer

Hence, $V (r) = 2 {πr}^{3} .$

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The volume $V$ of a right circular cylinder of height $h$ and radius $r$ is $V = {πr}^{2} h .$ If the height is twice the radius, express the volume $V$ as a function of $r$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

Step 3. Final Answer

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The volume Vof a right circular cylinder of height hand radius ris V=πr2h.If the height is twice the radius, express the volume V as a function of r.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

Step 3. Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

The volume $V$ of a right circular cylinder of height $h$ and radius $r$ is $V = {πr}^{2} h .$ If the height is twice the radius, express the volume $V$ as a function of $r$ .