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The surface area of the solid cone requiring paint rounded to the nearest whole number is how many square centimeters?

The surface area of the solid cone requiring paint rounded to the nearest whole number-example-1
User Wantobegeek
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1 Answer

22 votes
22 votes

In order to calculate the surface area of the cone, first let's calculate its slant height.

If the diameter is 5 cm, the radius is 2.5 cm. Now, using the Pythagorean theorem, we can calculate the slant height s:


\begin{gathered} s^2=h^2+r^2 \\ s^2=11.4^2+2.5^2 \\ s^2=129.96+6.25 \\ s^2=136.21 \\ s=11.67\text{ cm} \end{gathered}

Now, we can calculate the surface area using the formula below:


\begin{gathered} S=\pi rs+\pi r^2^{} \\ S=\pi\cdot2.5\cdot11.67+\pi\cdot2.5^2 \\ S=29.175\pi+6.25\pi \\ S=35.425\pi \\ S=111.29\text{ cm}^2 \end{gathered}

Rounding to the nearest square centimeter, we have a surface area of 111 cm².

User Simpleuser
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