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Type the correct answer in each box. Use numerals instead of words.The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.What is the surface area of the solid cone requiring paint to the nearest square centimeter?The surface area of the solid cone requiring paint rounded to the nearest whole number is square centimeters.

Sagot :

The surface area of a cone with diameter d and height h is given by:

[tex]A=\pi(\frac{d}{2})^2+\pi\cdot\frac{d}{2}\cdot\sqrt[]{h^2+(\frac{d}{2})^2}[/tex]

For d = 5 cm and h = 11.4 cm, we have:

[tex]\begin{gathered} A=\pi(\frac{5}{2})^2+\pi\frac{5}{2}\sqrt[]{11.4^2+(\frac{5}{2})^2} \\ A=\frac{25}{2}\pi+\pi\frac{25}{2}\sqrt[]{129.96+\frac{25}{2}} \\ A=12.5\pi+12.5\cdot\pi\cdot\sqrt[]{142.46} \\ A\approx12.5\pi+12.5\cdot11.94\cdot\pi \\ A\approx508cm^2 \end{gathered}[/tex]

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