Final answer:
The surface area of a pyramid with a square base of 0.7 km and a height of 500 m calculates to 1.19 sq km. None of the provided options (A, B, C, D) match this calculated value, which suggests a possible error in the question's options.
The right answer is C) 0.35 sq km
Step-by-step explanation:
To find the surface area of a pyramid with a square base, we need to calculate the area of the square base and the areas of the four triangular faces. The area of the base is easy to calculate since the base is a square: we simply square the length of one side.
The formula for the area of a square is side × side. So, for a base with a length of 0.7 km, the area is:
Area of base = 0.7 km × 0.7 km = 0.49 sq km.
Next, we need to calculate the area of one triangular face. The formula for the area of a triangle is 1/2 base × height. Each triangular face has a base of 0.7 km. However, we must convert the height from meters to kilometers before using the triangle area formula.
Height in kilometers = 500 m × (1 km/1000 m) = 0.5 km.
Area of one triangular face = 1/2 × 0.7 km × 0.5 km = 0.175 sq km.
Since there are four identical triangular faces, we multiply this area by four:
Total area of four triangular faces = 4 × 0.175 sq km = 0.7 sq km.
To find the total surface area of the pyramid, we add the area of the base to the total area of the triangular faces:
Total surface area of the pyramid = 0.49 sq km + 0.7 sq km = 1.19 sq km.
None of the options given (A, B, C, D) match this calculated value, which suggests there may be an error in the question or the provided options. When reporting this discrepancy, one should provide the process and the calculated value to the student for clarity.
The right answer is C) 0.35 sq km