Chapter 10: Q29. (page 629)

The lateral surface area Sof a cone can be found by using the formula $S = π r \sqrt{r^{2} + h^{2}}$ , 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:

$S = π r \sqrt{r^{2} + h^{2}}$ , 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 $S = π r \sqrt{r^{2} + h^{2}}$ and solve for h.

$S = π r \sqrt{r^{2} + h^{2}} 121 = π (3) \sqrt{3^{2} + h^{2}} \frac{121}{3 π} = \sqrt{9 + h^{2}} 12.84 = \sqrt{9 + h^{2}} {(12.84)}^{2} = {(\sqrt{9 + h^{2}})}^{2} 164.8656 = 9 + h^{2} 164.8656 - 9 = h^{2} 155.8656 = h^{2} \pm \sqrt{155.8656} = h \pm 12.48 = h$

As, the height of the cone cannot be negative, therefore $h = - 12.48$ 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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The lateral surface area Sof a cone can be found by using the formula $S = π r \sqrt{r^{2} + h^{2}}$ , 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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The lateral surface area Sof a cone can be found by using the formula S=πrr2+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

Pure Maths

Discrete Mathematics

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

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