Question

what is the surface area of this cone? round your answer to the nearest hundredth. 67 mm 42 mm square millimeters

Explanation:

Step1: Find the radius of the cone

The diameter of the base of the cone is given as 42 mm. The radius \( r \) is half of the diameter, so \( r=\frac{42}{2} = 21 \) mm.

Step2: Recall the formula for the surface area of a cone

The surface area \( SA \) of a cone is given by the formula \( SA=\pi r(r + l) \), where \( r \) is the radius and \( l \) is the slant height. Here, \( r = 21 \) mm and the slant height \( l=67 \) mm.

Step3: Substitute the values into the formula

Substitute \( r = 21 \) and \( l = 67 \) into the formula:
\[

$$\begin{align*} SA&=\pi\times21\times(21 + 67)\\ &=\pi\times21\times88\\ &=21\times88\times\pi\\ &=1848\pi \end{align*}$$

\]

Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( SA\approx1848\times3.14159 \approx 5804.54 \) (rounded to the nearest hundredth).

Answer:

\( 5804.54 \)