Q29. The lateral surface area S聽of a... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q29. (page 629)

The lateral surface area Sof a cone can be found by using the formula $S = 蟺 r \sqrt{r^{2} + h^{2}}$ , where r is the radius of the base and h is the height of the cone. Find the height of the cone.

Short Answer

Expert verified

The height of the given cone is $12.48 in.$

Step by step solution

Step 1. Write the formula for the lateral surface area of the cone.

The lateral surface area (S) of a cone is given by:

$S = 蟺 r \sqrt{r^{2} + h^{2}}$ , where r is the radius of the cone and h is the height of the cone.

Step 2. Observe the given diagram.

The given diagram is:

From the given diagram, it can be noticed that the lateral surface area (S) of a cone is $121 {in}^{2}$ and the radius of the cone (r) is 3 in.

Step 3. Find the height of the cone.

Substitute 121 for S and 3 for r in the equation $S = 蟺 r \sqrt{r^{2} + h^{2}}$ and solve for h.

$S = 蟺 r \sqrt{r^{2} + h^{2}} 121 = 蟺 (3) \sqrt{3^{2} + h^{2}} \frac{121}{3 蟺} = \sqrt{9 + h^{2}} 12.84 = \sqrt{9 + h^{2}} {(12.84)}^{2} = {(\sqrt{9 + h^{2}})}^{2} 164.8656 = 9 + h^{2} 164.8656 鈭� 9 = h^{2} 155.8656 = h^{2} 卤 \sqrt{155.8656} = h 卤 12.48 = h$

As, the height of the cone cannot be negative, therefore $h = 鈭� 12.48$ is not possible.

The only possible value h of is $12.48$ .

Therefore, the height of the cone is $12.48$ in.

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91影视

The lateral surface area Sof a cone can be found by using the formula $S = 蟺 r \sqrt{r^{2} + h^{2}}$ , where r is the radius of the base and h is the height of the cone. Find the height of the cone.

Short Answer

Step by step solution

Step 1. Write the formula for the lateral surface area of the cone.

Step 2. Observe the given diagram.

Step 3. Find the height of the cone.

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91影视

The lateral surface area Sof a cone can be found by using the formula S=蟺rr2+h2, where r is the radius of the base and h is the height of the cone. Find the height of the cone.

Short Answer

Step by step solution

Step 1. Write the formula for the lateral surface area of the cone.

Step 2. Observe the given diagram.

Step 3. Find the height of the cone.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Discrete Mathematics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

The lateral surface area Sof a cone can be found by using the formula $S = 蟺 r \sqrt{r^{2} + h^{2}}$ , where r is the radius of the base and h is the height of the cone. Find the height of the cone.