Math / Geometry

QuestionCalculate the Surface Area of the Cone Lcylle le \begin{tabular}{|l|l|l|l|l|l|} \hline Figure & $\pi$ & $r$ radius & $r^{2}$ & lislant height $S A=\pi r^{2}+\pi r l$ \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The cone has a circular base.
2. The radius of the base is $7$ cm.
3. The slant height of the cone is $19$ cm.
4. The formula for the surface area of a cone is given by $SA = \pi r^2 + \pi r l$ .

STEP 2

1. Recall the formula for the surface area of a cone.
2. Substitute the given values into the formula.
3. Calculate the surface area.

STEP 3

Recall the formula for the surface area of a cone:
$SA = \pi r^2 + \pi r l$

STEP 4

Substitute the given values for the radius $r = 7$ cm and slant height $l = 19$ cm into the formula:
$SA = \pi (7)^2 + \pi (7)(19)$

STEP 5

Calculate each term separately and then sum them:
1. Calculate $\pi (7)^2$ : $\pi (7)^2 = \pi \times 49$
2. Calculate $\pi (7)(19)$ : $\pi (7)(19) = \pi \times 133$
3. Sum the results: $SA = \pi \times 49 + \pi \times 133$ $SA = \pi (49 + 133)$ $SA = \pi \times 182$
4. Use the approximation $\pi \approx 3.14159$ to find the numerical value: $SA \approx 3.14159 \times 182$ $SA \approx 571.76938$
The surface area of the cone is approximately:
$\boxed{571.77 \text{ cm}^2}$

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