In the diagram, the base diameter is 14cm while the height is 12cm. Calculate the total surface area if the cylinder has both a base and a top.[\( \pi \frac...

Answer Details

To calculate the total surface area of the cylinder with both a base and a top, we need to find the area of the two bases and the lateral surface area. The area of one circular base is given by the formula πr², where r is the radius of the base. The diameter of the base is given as 14cm, so the radius is half of that, which is 7cm. Therefore, the area of one base is π(7cm)² = 49πcm². Since the cylinder has both a base and a top, the total area of the two bases is 2 × 49πcm² = 98πcm². The lateral surface area of the cylinder is given by the formula 2πrh, where r is the radius of the base and h is the height of the cylinder. Using the values given, we have r = 7cm and h = 12cm. Therefore, the lateral surface area is 2π(7cm)(12cm) = 168πcm². To get the total surface area, we add the area of the two bases to the lateral surface area. Thus, the total surface area of the cylinder is 98πcm² + 168πcm² = 266πcm². Now we need to simplify this expression, using the approximate value of π given to us as 22/7. So, 266πcm² ≈ 266 × (22/7) cm² ≈ 836cm². Therefore, the total surface area of the cylinder is approximately 836cm². Answer is the correct choice.