Question

maria has a metal candleholder, without a top, that has a height of 3 cm and a radius of 3 cm. how much metal was used to make the holder? 16π cm² 27π cm² 12π cm³ 12π cm²

Explanation:

Step1: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(2\pi rh\). Given \(r = 3\) cm and \(h=3\) cm, we have \(2\pi\times3\times3=18\pi\) \(cm^{2}\).

Step2: Calculate the area of the base

The formula for the area of a circle (base of the cylinder) is \(\pi r^{2}\). With \(r = 3\) cm, we get \(\pi\times3^{2}=9\pi\) \(cm^{2}\).

Step3: Find the total surface area (since there's no top)

The total surface area \(A\) of the candle - holder (no top) is the sum of the lateral surface area and the base area. So \(A=18\pi+9\pi = 27\pi\) \(cm^{2}\).

Answer:

\(27\pi\ cm^{2}\)