Use 3.14 as an approximation for p.
3. A cylinder with two open ends has a diameter of 4 centimetres and a height of
8 centimetres. Determine the outside surface area of the cylinder.
The radius of the cylinder is 2cm (diameter/2). The formula for the surface area of a cylinder is 2πr(h+r), where r is the radius and h is the height. Using 3.14 as an approximation for π, we can calculate the outside surface area as follows:
Surface Area = 2(3.14)(2)(8+2)
Surface Area = 2(3.14)(2)(10)
Surface Area = 125.6 cm²
Therefore, the outside surface area of the cylinder is approximately 125.6 cm².
To determine the outside surface area of the cylinder, we need to first calculate the lateral surface area and then add the areas of the two circular bases.
1. Calculate the lateral surface area:
The formula for the lateral surface area of a cylinder is given by: 2 * p * radius * height.
Given that the diameter is 4 centimeters, we can calculate the radius as half the diameter: 4 cm / 2 = 2 cm.
Substituting the values into the formula, we have: 2 * 3.14 * 2 cm * 8 cm = 100.48 cm².
2. Calculate the area of the circular bases:
The formula for the area of a circle is given by: p * radius^2.
Substituting the values into the formula, we have: 3.14 * 2 cm * 2 cm = 12.56 cm².
3. Calculate the total outside surface area:
To determine the outside surface area, we add the lateral surface area and the areas of the two circular bases: 100.48 cm² + 12.56 cm² + 12.56 cm² = 125.6 cm².
Therefore, the outside surface area of the cylinder is approximately 125.6 cm².