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Chapter 8: Problem 20

find the surface area of each cone. Round to nearest tenth. $$r=8.8 \mathrm{cm}, h=17.2 \mathrm{cm}$$

Short Answer

Expert verified
The surface area of the cone is approximately 772.8 \text{cm}^2.

Step by step solution

01

Identify the formula for the surface area

The surface area of a cone is given by the formula \(A = \pi r(r + l)\) where \(r\) is the radius, \(h\) is the height, and \(l\) is the slant height.
02

Calculate the slant height

To find the slant height \(l\), use the Pythagorean theorem: \(l = \sqrt{r^2 + h^2}\) Substitute \(r = 8.8 \text{cm}\) and \(h = 17.2 \text{cm}\): \[ l = \sqrt{(8.8)^2 + (17.2)^2} \approx 19.3 \text{cm}\]
03

Substitute the values into the surface area formula

Now substitute \(r = 8.8 \text{cm}\) and the calculated slant height \(l = 19.3 \text{cm}\) into the surface area formula: \[ A = \pi \cdot 8.8(8.8 + 19.3) \approx 772.8 \text{cm}^2 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

surface area of a cone
Understanding how to calculate the surface area of a cone is a fundamental topic in geometry. To find the surface area, we use the formula \( A = \pi r ( r + l ) \). Here's a step-by-step breakdown:
First, identify the variables: the radius (\

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