Question

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

Answer 1

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.