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 total surface area formula

The total surface area of a cone is the sum of the base area and the lateral (curved) surface area:
$$SA = \pi r^2 + \pi r l$$
where $r$ is the base radius, and $l$ is the slant height.

Step2: Substitute given values

Given $r=5$ cm, $l=13$ cm, $\pi=3.14$:
$$SA = (3.14 \times 5^2) + (3.14 \times 5 \times 13)$$

Step3: Calculate base area

Compute the area of the circular base:
$$3.14 \times 25 = 78.5$$

Step4: Calculate lateral surface area

Compute the curved surface area:
$$3.14 \times 65 = 204.1$$

Step5: Sum the two areas

Add the base area and lateral surface area:
$$78.5 + 204.1 = 282.6$$

Step6: Round to nearest whole number

Round the result to the nearest integer:
$$282.6 \approx 283$$

Answer:

283 cm²