Question

the circular base of a cone has a radius of 5 centimeters. the height of the cone is 12 centimeters, and the slant height is 13 centimeters. what is the approximate surface area of the cone? use 3.14 for π and round to the nearest whole number. 267 cm² 283 cm² 456 cm² 487 cm²

Explanation:

Step1: Recall the surface - area formula for a cone

The surface area formula of a cone is $S=\pi r(r + l)$, where $r$ is the radius of the base and $l$ is the slant height.

Step2: Substitute the given values into the formula

Given $r = 5$ cm and $l=13$ cm, and $\pi = 3.14$. Then $S=3.14\times5\times(5 + 13)$.

Step3: First, calculate the sum inside the parentheses

$5+13 = 18$.

Step4: Then, multiply the numbers

$S=3.14\times5\times18=3.14\times90 = 282.6$ $cm^{2}$.

Step5: Round to the nearest whole number

Rounding $282.6$ to the nearest whole number gives $283$ $cm^{2}$.

Answer:

$283$ $cm^{2}$