Chapter 5: Q. 72 (page 258)

The volume $V$ of a right circular cone is $V = \frac{1}{3} {πr}^{2} h .$ If the height is twice the radius, express the volume $V$ as a function of $r$ .

Short Answer

Expert verified

The Volume, $V (r) = \frac{2}{3} {πr}^{3} .$

Step by step solution

Step 1. Given Information

Given that $V = \frac{1}{3} {πr}^{2} h$ and $h (r) = 2 r .$

Step 2. Solution

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

Here, $V = \frac{1}{3} {πr}^{2} h, h (r) = 2 r .$

Now,

$V \circ h (r) = V (h (r)) V \circ h (r) = \frac{1}{3} {πr}^{2} {h (r)} V \circ h (r) = \frac{1}{3} {πr}^{2} {2 r} V \circ h (r) = \frac{2}{3} {πr}^{3} V (r) = \frac{2}{3} {πr}^{3}$

Step 3. Final answer

Hence, $V (r) = \frac{2}{3} {πr}^{3} .$

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The volume $V$ of a right circular cone is $V = \frac{1}{3} {πr}^{2} h .$ 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 cone is V=13πr2h.If the height is twice the radius, express the volume V as a function of r.

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Step 2. Solution

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The volume $V$ of a right circular cone is $V = \frac{1}{3} {πr}^{2} h .$ If the height is twice the radius, express the volume $V$ as a function of $r$ .