Question

bridget has a kitchen canister in the shape of a cylinder, which holds flour. if the canister is 24 cm in diameter and 26 cm tall, what is the surface area of the cylinder in terms of π? 624π cm² 1248π cm² 912π cm² 1236π cm²

Explanation:

Step1: Find the radius

The diameter $d = 24$ cm, so the radius $r=\frac{d}{2}=\frac{24}{2}=12$ cm.

Step2: Recall the surface - area formula for a cylinder

The surface - area formula of a cylinder is $S = 2\pi r^{2}+2\pi rh$, where $r$ is the radius and $h$ is the height.

Step3: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^{2}$. For two bases, $A_{bases}=2\pi r^{2}=2\pi\times(12)^{2}=2\pi\times144 = 288\pi$ $cm^{2}$.

Step4: Calculate the lateral - surface area

The lateral - surface area $A_{lateral}=2\pi rh$. Substitute $r = 12$ cm and $h = 26$ cm, we get $A_{lateral}=2\pi\times12\times26=624\pi$ $cm^{2}$.

Step5: Calculate the total surface area

$S=A_{bases}+A_{lateral}=288\pi + 624\pi=912\pi$ $cm^{2}$.

Answer:

$912\pi$ $cm^{2}$