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Analy
th grade > W. 6 Surface area of cones 5E6
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What is the surface area of this cone?
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Area of circles
Lesson: Surface area

$\Rightarrow$ $\newline$ int ism $\newline$ thent $\newline$ Strte $\newline$ ite: $\newline$ Astor: $\newline$ SixuE $\newline$ F $\newline$ Elsonter $\newline$ c. $\newline$ Conolitieth gemes $\newline$ Test Taks $\newline$ My IXL $\newline$ Learning $\newline$ Assessment $\newline$ Analy $\newline$ th grade > W. $6$ Surface area of cones $5$ E $6$ $\newline$ Learn with an example $\newline$ or $\newline$ Watch a video $\newline$ What is the surface area of this cone? $\newline$ Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\newline$ $\square$ square inches $\newline$ Submit $\newline$ Work it out $\newline$ Not feeling ready yet? These can help: $\newline$ Area of circles $\newline$ Lesson: Surface area

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int ism

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thent

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Strte

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ite:

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Astor:

\newline

SixuE

\newline

\newline

Elsonter

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\newline

Conolitieth gemes

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Test Taks

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My IXL

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Learning

\newline

Assessment

\newline

Analy

\newline

th grade > W.

6

Surface area of cones

5

6

\newline

Learn with an example

\newline

\newline

Watch a video

\newline

What is the surface area of this cone?

\newline

Use

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

\square

square inches

\newline

Submit

\newline

Work it out

\newline

Not feeling ready yet? These can help:

\newline

Area of circles

\newline

Lesson: Surface area

Find Slant Height: First, we need to find the slant height of the cone, which is not given. We can use the Pythagorean theorem for this, since we have the radius ( $5$ inches) and the height ( $12$ inches). The slant height will be the hypotenuse of the right triangle formed by the height, radius, and slant height of the cone.
Calculate Slant Height: Using the Pythagorean theorem: slant height $l^2$ = radius $r^2$ + height $h^2$ . So, $l^2 = 5^2 + 12^2$ , which means $l^2 = 25 + 144$ . Therefore, $l^2 = 169$ .
Calculate Lateral Surface Area: Now, we take the square root of both sides to find the slant height: $l = \sqrt{169}$ , which means $l = 13$ inches.
Calculate Base Area: Next, we calculate the lateral surface area of the cone, which is $\pi * r * l$ . So, lateral surface area = $3.14 * 5 * 13$ .
Calculate Total Surface Area: Calculating the lateral surface area gives us $3.14 \times 5 \times 13 = 204.1$ square inches.
Calculate Total Surface Area: Calculating the lateral surface area gives us $3.14 \times 5 \times 13 = 204.1$ square inches.Now, we need to add the base area of the cone to the lateral surface area to get the total surface area. The base area is a circle with radius $5$ inches, so base area $= \pi \times r^2$ .
Calculate Total Surface Area: Calculating the lateral surface area gives us $3.14 \times 5 \times 13 = 204.1$ square inches.Now, we need to add the base area of the cone to the lateral surface area to get the total surface area. The base area is a circle with radius $5$ inches, so base area = $\pi \times r^2$ .Calculating the base area gives us $3.14 \times 5^2 = 3.14 \times 25 = 78.5$ square inches.
Calculate Total Surface Area: Calculating the lateral surface area gives us $3.14 \times 5 \times 13 = 204.1$ square inches.Now, we need to add the base area of the cone to the lateral surface area to get the total surface area. The base area is a circle with radius $5$ inches, so base area = $\pi \times r^2$ .Calculating the base area gives us $3.14 \times 5^2 = 3.14 \times 25 = 78.5$ square inches.Finally, we add the lateral surface area and the base area to get the total surface area of the cone. Total surface area = $204.1 + 78.5$ .
Calculate Total Surface Area: Calculating the lateral surface area gives us $3.14 \times 5 \times 13 = 204.1$ square inches.Now, we need to add the base area of the cone to the lateral surface area to get the total surface area. The base area is a circle with radius $5$ inches, so base area = $\pi \times r^2$ .Calculating the base area gives us $3.14 \times 5^2 = 3.14 \times 25 = 78.5$ square inches.Finally, we add the lateral surface area and the base area to get the total surface area of the cone. Total surface area = $204.1 + 78.5$ .Adding them up, we get a total surface area of $204.1 + 78.5 = 282.6$ square inches. We round this to the nearest hundredth, which gives us $282.60$ square inches.