Chapter 3: Q 5. (page 298)

Give formulas for the volume and the surface area of a cylinder whose radius $r$ is half of its height $h$ .

Short Answer

Expert verified

Volume of cylinder is $V = \frac{π h^{3}}{4}$ .

Surface area of cylinder is $S = \frac{3 π h^{2}}{2}$ .

Step by step solution

Step 1. Standard formulas

The volume and surface area of a right circular cylinder of radius $r$ and height $h$ are

$V = π r^{2} h$

$S = 2 π r h + 2 π r^{2}$

Step 2. Substitution and solution

Now given that the height is $h$ and radius is half of its height means $r = \frac{h}{2}$ of cylinder

Substitute in standard formulas we get,

Volume of cylinder is $V = π {(\frac{h}{2})}^{2} h = \frac{π h^{3}}{4}$ .

Surface area of cylinder is $S = 2 π \frac{h}{2} h + 2 π {(\frac{h}{2})}^{2} = π h^{2} + \frac{π h^{2}}{2} = \frac{3 π h^{2}}{2}$

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Give formulas for the volume and the surface area of a cylinder whose radius $r$ is half of its height $h$ .

Short Answer

Step by step solution

Step 1. Standard formulas

Step 2. Substitution and solution

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Give formulas for the volume and the surface area of a cylinder whose radius r is half of its height h.

Short Answer

Step by step solution

Step 1. Standard formulas

Step 2. Substitution and solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Probability and Statistics

Geometry

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Give formulas for the volume and the surface area of a cylinder whose radius $r$ is half of its height $h$ .