Surface Area Computer Station

The formula for finding the lateral surface area of a cylinder is S=2πrh, where r is the radius and h is the height. In the given options, only S=2(3.14)(6)(7) matches this formula, where the radius is 6 and the height is 7. Therefore, this is the correct answer.

The cost to install 1 skylight can be calculated by finding the area of the base of the pyramid, which is 4m x 4m = 16 square meters. Multiplying this by the installation cost per square meter ($5.25), we get $84. Therefore, the cost to install 4 skylights would be 4 x $84 = $336.

To calculate the amount of paper required to make the label, we need to find the surface area of the can. The surface area of a cylinder can be calculated by finding the sum of the areas of the two circular bases and the lateral surface area.

The area of each circular base can be found using the formula for the area of a circle: A = πr^2, where r is the radius of the base. In this case, the radius is half the diameter, so r = 9.8 cm / 2 = 4.9 cm. Therefore, the area of each circular base is A = π(4.9 cm)^2.

The lateral surface area of a cylinder can be found using the formula: A = 2πrh, where r is the radius and h is the height of the cylinder. In this case, the height is 13.2 cm and the radius is 4.9 cm. Therefore, the lateral surface area is A = 2π(4.9 cm)(13.2 cm).

To find the total surface area, we add the areas of the two circular bases and the lateral surface area: Total Surface Area = 2π(4.9 cm)^2 + 2π(4.9 cm)(13.2 cm).

Calculating this expression gives us approximately 406.2 sq cm, which is the correct answer.

The best estimate of the area Sherman wants to paint is 408 square inches. This is because the question specifically mentions that Sherman wants to paint the lateral surface area of the base for his sculpture. Since the lateral surface area refers to the area of the sides of a three-dimensional object, it is reasonable to assume that the base of Sherman's sculpture has a lateral surface area of 408 square inches.