The surface area, the lateral area and the volume are, respectively:
- S = 100 mi², L = 200 mi², V = 500 mi³
- S ≈ 201.062 cm², L ≈ 508.938 cm², V ≈ 1809.558 cm³
- S = 139.5 km², L = 180 km², V = 558 km³
- S = 6 km², L = 108 km², V = 54 km³
How to determine the volume, the lateral area and the surface area of each solid
The volume is a measure of the space occupied by the solid, the lateral area is the measure of the area occupied by lateral faces of the solid and the surface area is the area occupied by the cross section of the solid. Please notice that the volume of each prism is equal to the product of the surface area and the height of the solid and the lateral area is the sum of the areas of the lateral faces.
In this exercise we must follow these steps to obtain the required results:
- Calculate the surface area.
- Calculate the lateral area.
- Calculate the volume.
Lastly, we proceed to make the corresponding calculations:
Surface area - Figure 1
S = (10 mi)² = 100 mi²
Lateral area - Figure 1
L = 4 · (10 mi) · (5 mi) = 200 mi²
Volume - Figure 1
V = S · h = (100 mi²) · (5 mi) = 500 mi³
Surface area - Figure 2
S = 0.25 π · (16 cm)² ≈ 201.062 cm²
Lateral area - Figure 2
L = π · (18 cm) · (9 cm) ≈ 508.938 cm²
Volume - Figure 2
V = S · h = (201.062 cm²) · (9 cm) ≈ 1809.558 cm³
Surface area - Figure 3
S = 0.5 · (5) · (9 km) · (6.2 km) = 139.5 km²
Lateral area - Figure 3
L = (5) · (4 km) · (9 km) = 180 km²
Volume - Figure 3
V = S · h = (139.5 km²) · (4 km) = 558 km³
Surface area - Figure 4
S = 0.5 · (3 km) · (4 km) = 6 km²
Lateral area - Figure 4
L = (9 km) · (3 km) + (9 km) · (4 km) + (9 km) · (5 km) = 108 km²
Volume - Figure 4
V = S · h = (6 km²) · (9 km) = 54 km³
To learn more on volumes, we kindly invite to check this verified question: https://brainly.com/question/1578538
