Surface Area Computer Station

1)

Which of the following could be used to find the lateral surface area of the cylinder below?

S= 2(3.14)(12)(14)

S= 2(3.14)(3)(14)

S=2(3.14)(6)(7)

S=(3.14)(6)(14)

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.

Explanation

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.

2) Find the surface area of the figure above.

.

126 square centimeters

132 square centimeters

120 square centimeters

144 square centimeters

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Explanation

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3) A can of vegetables has a diameter of 9.8 cm and is 13.2 cm tall. How much paper is required to make the label assuming there is no overlap? Round answer to the nearest tenth.

203.1 sq cm

406.2 sq cm

557.0 sq cm

812.4 sq cm

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.

Explanation

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.

4)

Sherman wants to paint the lateral surface area of the base for a sculpture he made. Which is the best estimate of the area Sherman wants to paint?

51 square inches

136 square inches

408 square inches

533 square inches

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.

Explanation

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.

5) A skylight is shaped like a square pyramid. Each panel has a 4 m base. The slant height is 2 m, and the base is open. The installation cost is $5.25 per square meter. What is the cost to install 4 skylights?

$84

$159

$218

$336

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.

Explanation

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.