how do i find the lateral height **Calculating the Surface Area of a Right Circular Cone**This educational resource explains how to calculate the surface area of a right circular cone given its dimensions.### Diagram Explanation:The diagram provided represents a right circular cone with the following dimensions:- The height (h) of the cone is 4 inches.- The radius (r) of the base of the cone is 6 inches. ### Steps to Calculate the Surface Area:The surface area of a right circular cone consists of two parts:1. **Lateral Surface Area (LSA)**: The area of the cone's slanted surface.2. **Base Surface Area (BSA)**: The area of the cone's circular base.#### 1. Lateral Surface Area (LSA):To calculate the Lateral Surface Area, we use the formula:\[ \text{LSA} = \pi r l \]where $ l $ is the slant height of the cone.To find the slant height $ l $, we use the Pythagorean theorem:\[ l = \sqrt{r^2 + h^2} \]Substituting the given dimensions:\[ l = \sqrt{6^2 + 4^2} \]\[ l = \sqrt{36 + 16} \]\[ l = \sqrt{52} \]\[ l \approx 7.21 \, \text{inches} \]Now, calculating the LSA:\[ \text{LSA} = \pi \cdot 6 \cdot 7.21 \]\[ \text{LSA} \approx 135.78 \, \text{in}^2 \]#### 2. Base Surface Area (BSA):To calculate the Base Surface Area, we use the formula:\[ \text{BSA} = \pi r^2 \]Substituting the given dimensions:\[ \text{BSA} = \pi \cdot 6^2 \]\[ \text{BSA} = \pi \cdot 36 \]\[ \text{BSA} \approx 113.1 \, \text{in}^2 \]### Total Surface Area (TSA):The total surface area of the cone is the sum of the lateral and base surface areas:\[ \text{TSA} = \text{LSA} + \text{

Answered: how do i find the lateral height

Math

Geometry

how do i find the lateral height

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

See similar textbooks

Related questions

Q: What is parametric equation?

Q: Describe the relationship between the point (3, 11) and the vector (3,11).

Q: nd the length of the vector fo raight line joining the points 5,2). Also find the angle made

A: Given, The vector is formed by the straight line joining the points 1,3 and5,2. The length is to be…

Q: Convert into rectangular coordinates. (2,-) 3

Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

Q: how do you write in parametric form?

Q: M] - [8] x+y -3x+y.

Q: Check picture 12, where do I plug the two lines ??

Q: Determine the direction in which f = x²y√z has maximum rate of increase from P = (8,3,8). Express…

Q: How can we find the cartesian equation from a vector equation?

A: Equation of line in vector form is:r→=a→+λb→Where,a→=x1i→+y1j→+z1k→ b→=b1i→+b2j→+b3k→

Q: 6x Find -dA, where R is the parallelogram enclosed by the lines 4x – 3y 6x – y = 0, 6x – y = 9, – 4x…

Q: calculate the distance between the point P (2, 3) and the point Q (1,-2) 20 3 us O V25 4 jus O V26

A: The distance between two points (x1, y1) and (x2, y2) is d=(x2-x1)2+(y2-y1)2…

Q: Describe the plane x = 4.

A: Given, plane x=4we have to describe the plane x=4

Q: Find parametric equations for the line in which the planes, X+2y-2z=5 and 5x-2y-z=0 intersects. Show…

Q: Two forces of magnitudev50N and 20N act on an object at 30 and -45 degrees with the positive x axis.…

A: Image is attached with detailed solution.

Q: draw the line which start point (1,1,0) and end point (3,4,0)by using parametric equation

Q: This is grade 12 calculus/vectors (planes and line intersection unit) please write it on paper…

Q: spherical: (3, * , ) Change to rectangular.

A: Given,Spherical coordinates: 3,3π4,π3

Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

100%

how do i find the lateral height

**Calculating the Surface Area of a Right Circular Cone**

This educational resource explains how to calculate the surface area of a right circular cone given its dimensions.

### Diagram Explanation:

The diagram provided represents a right circular cone with the following dimensions:
- The height (h) of the cone is 4 inches.
- The radius (r) of the base of the cone is 6 inches.

### Steps to Calculate the Surface Area:

The surface area of a right circular cone consists of two parts:
1. **Lateral Surface Area (LSA)**: The area of the cone's slanted surface.
2. **Base Surface Area (BSA)**: The area of the cone's circular base.

#### 1. Lateral Surface Area (LSA):
To calculate the Lateral Surface Area, we use the formula:
\[ \text{LSA} = \pi r l \]
where $ l $ is the slant height of the cone.

To find the slant height $ l $, we use the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]

Substituting the given dimensions:
\[ l = \sqrt{6^2 + 4^2} \]
\[ l = \sqrt{36 + 16} \]
\[ l = \sqrt{52} \]
\[ l \approx 7.21 \, \text{inches} \]

Now, calculating the LSA:
\[ \text{LSA} = \pi \cdot 6 \cdot 7.21 \]
\[ \text{LSA} \approx 135.78 \, \text{in}^2 \]

#### 2. Base Surface Area (BSA):
To calculate the Base Surface Area, we use the formula:
\[ \text{BSA} = \pi r^2 \]

Substituting the given dimensions:
\[ \text{BSA} = \pi \cdot 6^2 \]
\[ \text{BSA} = \pi \cdot 36 \]
\[ \text{BSA} \approx 113.1 \, \text{in}^2 \]

### Total Surface Area (TSA):
The total surface area of the cone is the sum of the lateral and base surface areas:
\[ \text{TSA} = \text{LSA} + \text{

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ratios$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.