What is the lateral surface area of a solid 8 meters high

whose base is the figure at right? Dimensions are in meters.
(A)5522 m2
(B)820 m2
(C)870 m2
(D) 922.8 m2

The image is a square in the middle that is 12x15 meters, and two half cylinders next to it, one with a radius of 15 and another with a radius of 10.

Is it c?

Hard to say, since you don't say how the semicircles tuck up against the rectangle. But the lateral area would be the height times the sum of the exposed perimeters on the base.

To find the lateral surface area of the given solid, we need to calculate the sum of the surface areas of all the lateral faces.

From the description, we have a square prism in the middle with dimensions 12x15 meters, which means it has two faces of dimensions 12x15, and four faces of dimensions 8x12 (the height of the solid). These face areas can be calculated as:

Area of one 12x15 face = 12 * 15 = 180 m²
Area of one 8x12 face = 8 * 12 = 96 m²

So, the total area of all the square prism faces is (2 * 180) + (4 * 96) = 552 m².

Next, we have two half-cylinders. One has a radius of 15 meters, and the other has a radius of 10 meters. The lateral surface area of a cylinder is given by the formula 2πrh, where r is the radius and h is the height. Since we have half-cylinders, we need to calculate the lateral surface area for each and then divide by 2.

For the half-cylinder with a radius of 15:
Lateral surface area = (2 * π * 15 * 8) / 2 = 240π m²

For the half-cylinder with a radius of 10:
Lateral surface area = (2 * π * 10 * 8) / 2 = 160π m²

Now, we can calculate the total lateral surface area by adding up the surface areas of the square prism and the two half-cylinders:
Total lateral surface area = 552 m² + 240π m² + 160π m²

To determine the approximate value for the lateral surface area, we can use 3.14 as an approximation for π. Evaluating the expression, we have:
Total lateral surface area ≈ 552 m² + 240 * 3.14 m² + 160 * 3.14 m²
≈ 552 m² + 753.6 m² + 502.4 m²
≈ 1808 m²

The calculated lateral surface area is approximately 1808 m².

Therefore, the correct option among the given choices is not (C) 870 m², but rather the closest option is (A) 5522 m².