Use 3.14 as pi. Use the ormula A= pi x radius squared. Mrs. Thomson buys a cylindrical speaker with a diameter of 6 centimetres and a height of 21 centimetres. She wants to wrap the speaker with a protection cover, leaving one end of the circular part open. Determine the area of the speaker to be covered.
First, we need to find the radius of the speaker, which is half of its diameter:
radius = 6 cm / 2 = 3 cm
Next, we can use the formula for the area of a cylinder:
A = pi x radius^2 x height
A = 3.14 x 3^2 x 21
A = 3.14 x 9 x 21
A = 592.86 cm^2
Therefore, the area of the speaker to be covered is approximately 592.86 square centimetres.
To determine the area of the speaker to be covered, we need to find the surface area of the cylindrical part of the speaker, excluding one end.
1. Start by finding the radius of the circular base of the cylinder. The diameter is given as 6 centimeters, so the radius is half of that, which is 6/2 = 3 centimeters.
2. Next, calculate the area of the circular base of the cylinder using the formula A = πr^2. Substituting the values, we have A = 3.14 x (3^2) = 3.14 x 9 = 28.26 square centimeters.
3. The next step is to calculate the lateral surface area of the cylinder, which is given by the formula A = 2πrh, where r is the radius and h is the height. Substituting the values, we have A = 2 x 3.14 x 3 x 21 = 395.64 square centimeters.
4. Finally, add the area of the circular base and the lateral surface area to get the total surface area of the cylinder (excluding one end). A = 28.26 + 395.64 = 423.90 square centimeters.
Therefore, the area of the speaker to be covered is 423.90 square centimeters.