4.5 inches circle and this is the radius
10.2 inches this is one side of the rectangle
4.5 inches bottom circle radius
Simone has a red cylindrical storage box that she would like to decorate with patterned paper. The radius of the box is 4.5 inches and the height is 10.2 inches. The cylinder’s net is shown below. How much paper will Simone need to cover the entire box? (Use 3.14 for
74.16 square inches
74.16 square inches
206.55 square inches
206.55 square inches
415.42 square inches
415.42 square inches
648.57 square inch
648.57 square inches
To find the surface area of the cylinder, we first need to find the area of the two circles at the top and bottom. The formula for the area of a circle is A = πr^2, where r is the radius. Since the radius is 4.5 inches, the area of each circle is:
A = 3.14 * (4.5)^2 = 3.14 * 20.25 = 63.585 square inches
Since there are two circles, the total area for the top and bottom circles is:
2 * 63.585 = 127.17 square inches
Next, we need to find the area of the side of the cylinder. The formula for the lateral surface area of a cylinder is A = 2πrh, where r is the radius and h is the height. Plugging in the values:
A = 2 * 3.14 * 4.5 * 10.2 = 2 * 3.14 * 45.9 = 288.612 square inches
Therefore, the total surface area of the cylinder is:
127.17 + 288.612 = 415.782 square inches
So, Simone will need 415.782 square inches of paper to cover the entire box.